1. Agudelo, Oscar; Del Pino, Manuel; Wei, Juncheng, Catenoidal layers for the Allen-Cahn equation in bounded domains, Chin. Ann. Math. Ser. B 38 (2017), no. 1, 13–44. (arxiv)
  2. Agudelo, Oscar; del Pino, Manuel; Wei, Juncheng, Higher dimensional catenoid, Liouville equation and Allen-Cahn equation. To appear in Int. Math. Res. Notices. (pdf)
  3. Alejo, Miguel A.; Muñoz, Claudio; Palacios, José M.  On the variational structure of breather solutions I: Sine-Gordon equation.J. Math. Anal. Appl. 453 (2017), no. 2, 1111–1138.
  4. Alejo, Miguel A.; Muñoz, Claudio; Palacios, José M. On the variational structure of breather solutions II: Periodic mKdV equation.  Electron.  J.  Differential Equations, Paper No. 56, 26 pp.
  5. Barchiesi, Marco; Henao, Duvan; Mora-Corral, Carlos; Local invertibility in Sobolev spaces with applications to nematic elastomers and magnetoelasticity. Arch. Ration. Mech. Anal. 224 (2017), no. 2, 743–816. (pdf)
  6. Barles, Guy; Ley, Olivier; Topp, Erwin Lipschitz regularity for integro-differential equations with coercive Hamiltonians and application to large time behaviour.Nonlinearity 30 (2017), no. 2, 703–734.
  7. Barrios, Begoña; Del Pezzo, Leandro; García-Melián, Jorge; Quaas, Alexander  A Liouville theorem for indefinite fractional diffusion equations and its application to existence of solutions. Discrete Contin. Dyn. Syst. 37 (2017), no. 11, 5731–5746.
  8. Barrios, B.; Del Pezzo, L.; García-Melián, J.; Quaas, A.; Monotonicity of solutions for some nonlocal elliptic problems in half-spaces. Calc. Var. Partial Differential Equations 56 (2017), no. 2, 56:39. (pdf)
  9. Barrios, Begoña; Del Pezzo, Leandro; García-Melián, Jorge; Quaas, Alexander,  A priori bounds and existence of solutions for some nonlocal elliptic problems; to appear in Rev. Iberoamericana. (pdf)
  10. Benguria, Rafael D.; Fournais, Søren; Stockmeyer, Edgardo; Van Den Bosch, Hanne Self-adjointness of two-dimensional Dirac operators on domains.  Ann. Henri Poincaré 18 (2017), no. 4, 1371–1383.
  11. Benguria, Rafael D.; Fournais, Søren; Stockmeyer, Edgardo; Van Den Bosch, Hanne Spectral gaps of Dirac operators describing graphene quantum dots. Math. Phys. Anal. Geom. 20 (2017), no. 2, Art. 11, 12 pp.
  12. Chipot, Michel; Dávila, Juan; del Pino, Manuel; On the behavior of positive solutions of semilinear elliptic equations in asymptotically cylindrical domains, J. Fixed Point Theory Appl. 19 (2017), no. 1, 205–213.
  13. Clerc, Marcel G.; Dávila, Juan Diego; Kowalczyk, Michał; Smyrnelis, Panayotis; Vidal-Henriquez, Estefania Theory of light-matter interaction in nematic liquid crystals and the second Painlevé equation Calc. Var. Partial Differential Equations 56 (2017), no. 4, Art. 93, 22 pp.
  14. P. Daskalopoulos, M. del Pino, N. Sesum Type II ancient compact solutions to the Yamabe flow. To appear in J. Reine Angel. Math. DOI: https://doi.org/10.1515/crelle-2015-0048.
  15. Dávila, Gonzalo; Quaas, Alexander; Topp, Erwin Continuous viscosity solutions for nonlocal Dirichlet problems with coercive gradient terms Math. Ann. 369 (2017), no. 3-4, 1211–1236.
  16. Dávila, Juan; del Pino, Manuel; Nguyen, Xuan Hien Finite topology self-translating surfaces for the mean curvature flow in ℝ3.Adv. Math. 320 (2017), 674–729.
  17. Juan Dávila, Jorge Faya, Fethi Mahmoudi, New type of solutions to a slightly subcritical Hénon type problem on general domains. J. Differential Equations 263 (2017), no. 11, 7221–7249. (pdf)
  18. Dávila, J.; del Pino, M: & Wei, J., Nonlocal s-minimal surfaces and Lawson cones, to appear in Journal of Differential Geometry. (arxiv).
  19. Juan Dávila, Louis Dupaigne, Juncheng Wei, On the fractional Lane-Emden equation. Trans. Amer. Math. Soc. 369 (2017), no. 9, 6087–6104. (pdf)
  20. Dávila, Juan; López Ríos, Luis; Sire, Yannick, Bubbling solutions for nonlocal elliptic problems.  To appear in Rev. Mat. Iberoamericana. (arxiv)
  21. A. De la Torre, M. del Pino, M.d.M. Gonzalez, J. Wei, Delaunay-type singular solutions for the fractional Yamabe Problem. To appear in Math Annalen. (pdf)
  22. Del Pezzo, Leandro M.; Quaas, Alexander; A Hopf’s lemma and a strong minimum principle for the fractional Laplacian, J. Differential Equations 263 (2017), no. 1, 765–778. (arxiv)
  23. Del Pezzo, Leandro M.; Quaas, Alexander; Non-resonant Fredholm alternative and anti-maximum principle for the fractional p-Laplacian. J. Fixed Point Theory Appl.19 (2017), no. 1, 939–958. (arxiv)
  24. Manuel del Pino, Konstantinos T. Gkikas, Ancient shrinking spherical interfaces in the Allen-Cahn Equation. To appear Proc Roy Soc Edinburgh. (arxiv)
  25. M. del Pino, M. Musso, C. Roman, J. Wei, Interior bubbling solutions for the critical Lin-Ni-Takagi problem in dimension 3. To appear in J. d’Analyse Mathemathique. Preprint arXiv:1512.03468. (arxiv)
  26. González-Melendez, Osiris; Quaas, Alexander; On critical exponents for Lane–Emden–Fowler-type equations with a singular extremal operator. Ann. Mat. Pura Appl. (4) 196 (2017), no. 2, 599–615. (researchgate)
  27. Henao, Duvan; Majumdar, Apala; Pisante, Adriano; Uniaxial versus biaxial character of nematic equilibria in three dimensions. Calc. Var. Partial Differential Equations 56 (2017), no. 2, 56:55. (arxiv)
  28. Zied Khemiri, Fethi Mahmoudi, Abdelattif Messaoudi, Concentration on submanifolds for an Ambrosetti-Prodi type problem, . Calc. Var. Partial Differential Equations 56 (2017), no. 2, Art. 19, 40 pp.  (pdf).
  29. Kim, Seunghyeok; Musso, Monica; Wei, Juncheng A non-compactness result on the fractional Yamabe problem in large dimensions.  J. Funct. Anal. 273 (2017), no. 12, 3759–3830.
  30. Michal Kowalczyk, Yvan Martel, Claudio Muñoz, Nonexistence of small, odd breathers for a class of nonlinear wave equations. Lett. Math. Phys. 107 (2017), no. 5, 921–931. (arxiv).
  31. Michal Kowalczyk, Yvan Martel, Claudio Muñoz, Kink dynamics in the phi^4 model: asymptotic stability for odd perturbations in the energy space. J. Amer. Math. Soc. 30 (2017), no. 3, 769–798. (arxiv).
  32. C. Muñoz, Instability in nonlinear Schrodinger breathers, accepted for publication in  Proyecciones (arxiv).
  33. Musso, Monica; Sign-changing blowing-up solutions for a non-homogeneous elliptic equation at the critical exponent. J. Fixed Point Theory Appl. 19 (2017), no. 1, 345–361. (researchgate)
  34. Nam, Phan Thành; Van Den Bosch, Hanne Nonexistence in Thomas–Fermi–Dirac–von Weizsäcker theory with small nuclear charges. Math. Phys. Anal. Geom. 20 (2017), no. 2, Art. 6, 32 pp.
  35. Alexander Quaas, Erwin Topp, Existence and Uniqueness of Large Solutions for a Class of Non Uni- formly Elliptic Semilinear Equations, to appear in Journal d’Analyse Math. pdf
  36. Topp, Erwin; Yangari, Miguel Existence and uniqueness for parabolic problems with Caputo time derivative. J. Differential Equations 262 (2017), no. 12, 6018–6046.
  37. Xia, Aliang; Quaas, Alexander; Existence and uniqueness of positive solutions for a class of logistic type elliptic equations in R^N involving fractional Laplacian. Discrete Contin. Dyn. Syst. 37 (2017), no. 5, 2653–2668. (researchgate)

  1.  Abdellaoui, Boumediene; Mahmoudi, Fethi; An improved Hardy inequality for a nonlocal operator, DCDS-A, Vol. 36, No. 3, 2016.
  2. Alarcón, Salomón; Burgos-Pérez, Miguel Ángel; García-Melián, Jorge; Quaas, Alexander Nonexistence results for elliptic equations with gradient terms. J. Differential Equations 260 (2016), no. 1, 758–780. (pdf)
  3. Alarcón, Salomón; Burgos-Pérez, Miguel Ángel; García-Melián, Jorge; Quaas, Alexander, Classification of supersolutions and Liouville theorems for some nonlinear elliptic problem, Discrete and Continuous Dynamical System – A Volume 36, Number 9, September 2016 pp. 4703-4721. (pdf)
  4. Alarcón, Salomón; García-Melián, Jorge; Quaas, Alexander, Optimal Liouville theorems for supersolutions of elliptic equations with the Laplacian. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 16 (2016), no. 1, 129–158. (pdf)
  5. Ao, Weiwei; Musso, Monica; Pacard, Frank; Wei, Juncheng, Solutions without any symmetry for semilinear elliptic problems. J. Funct. Anal. 270 (2016), no. 3, 884–956. (arxiv)
  6. J.-F. Babadjian, D. Henao: Reduced models for linearly elastic thin films allowing for fracture, debonding or delamination, Interfaces and Free Boundaries 18, no. 4 (2016), 545–578.
  7. Chen, Wenjing; Dávila, Juan; Guerra, Ignacio Bubble tower solutions for a supercritical elliptic problem in R^N. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 15 (2016), 85–116. pdf
  8. Cinti, Eleonora; Davila, Juan; Del Pino, Manuel; Solutions of the fractional Allen–Cahn equation which are invariant under screw motion. J. Lond. Math. Soc. (2) 94 (2016), no. 1, 295–313. pdf
  9. Côte, Raphaël; Muñoz, Claudio; Pilod, Didier; Simpson, Gideon, Asymptotic stability of high-dimensional Zakharov-Kuznetsov solitons. Arch. Ration. Mech. Anal. 220 (2016), no. 2, 639–710. (arxiv)
  10. Daskalopoulos, Panagiota; del Pino, Manuel; King, John; Sesum, Natasa, New type I ancient compact solutions of the Yamabe flow. Nonlinear Anal. 137 (2016), 338–356. (arxiv)
  11. Dávila, Juan; del Pino, Manuel; Dipierro, Serena; Valdinoci, Enrico Nonlocal Delaunay surfaces. Nonlinear Anal. 137 (2016), 357–380. pdf
  12. Dávila, Juan;  del Pino,  Manuel; Dipierro, Serena; Valdinoci, Enrico , Concentration phenomena for the nonlocal Schrödinger equation with Dirichlet datum. Anal. PDE 8 (2015), no. 5, 1165–1235. (arxiv)
  13. Dávila, Juan; Guerra, Ignacio; Slowly decaying radial solutions of an elliptic equation with subcritical and supercritical exponents. J. Anal. Math. 129 (2016), 367–391. pdf
  14. Davila, Gonzalo;  Topp; Erwin; Quaas, Alexander,  Continuous viscosity solutions  nonlocal Dirichlet problems with coercive gradient terms. Math. Ann. DOI 10.1007/s00208-016-1481-3. pdf
  15. Dávila, Juan; Wang, Kelei; Wei, Juncheng Qualitative analysis of rupture solutions for a MEMS problem. Ann. Inst. H. Poincaré Anal. Non Linéaire 33 (2016), no. 1, 221–242. pdf
  16. Del Pezzo, Leandro; Quaas, Alexander; Global Bifurcation for Fractional p-Laplacian and an Application. Z. Anal. Anwend. 35 (2016), no. 4, 411–447. pdf
  17. Del Pezzo, Leandro .; Quaas, Alexander, Global Bifurcation for Fractional p-Laplacian and an Application. Z. Anal. Anwend. 35 (2016), no. 4, 411–447.
  18. del Pino, Manuel; Pistoia, Angela; Vaira, Giusi; Large mass boundary condensation patterns in the stationary Keller–Segel system. J. Differential Equations 261 (2016), no. 6, 3414–3462. (arxiv)
  19. Deng, Shengbing; Musso, Monica; Pistoia, Angela; Concentration on minimal submanifolds for a Yamabe-type problem. Comm. Partial Differential Equations 41 (2016), no. 9, 1379–1425. (arxiv)
  20. Deng, Shengbing; Mahmoudi, Fethi; Musso, Monica, Bubbling on boundary submanifolds for a semilinear Neumann problem near high critical exponents. Discrete Contin. Dyn. Syst. 36 (2016), no. 6, 3035–3076.
  21. Jorge García-Melián,  Alexander Quaas, Boyan Sirakov, Elliptic Equation with absorption in the half space, Bull Braz Math Soc, New Series 47 (3), 811-821.
  22. Danilo Garrido, Monica Musso, Entire sign-changing solutions with finite energy to the fractional Yamabe equation. Pacific J. Math. 283 (2016), no. 1, 85–114.
  23. Osiris González-Melendez,  Alexander Quaas,  On critical exponents for Lane-Emden-Fowler-type equations with a singular extremal operator, Annali di Matematica, DOI 10.1007/s10231-016-0588-1. pdf
  24. Duván Henao, Carlos Mora-Corral, Xianmin Xu,  A numerical study of void coalescence and fracture in nonlinear elasticity. Comput. Methods Appl. Mech. Engrg. 303 (2016), 163–184.
  25. Isabella Ianni, Monica Musso, Angela Pistoia, Blow-up for sign-changing solutions of the critical heat equation in domains with a small hole. Commun. Contemp. Math. 18 (2016), no. 1, 1550017, 18 pp.
  26. Anna Kazeykina, Claudio Muñoz, Dispersive estimates for rational symbols and local well-posedness of the nonzero energy NV equation. J. Funct. Anal. 270 (2016), no. 5, 1744–1791. (arxiv)
  27. Mahmoudi, Fethi; Nouaili, Nejla; Zaag, Hatem Construction of a stable periodic solution to a semilinear heat equation with a prescribed profile. Nonlinear Anal. 131 (2016), 300–324. (arxiv)
  28. Claudio Muñoz, The Gardner equation and the stability of multi-kink solutions of the mKdV equation. Discrete Contin. Dyn. Syst. 36 (2016), no. 7, 3811–3843. (arxiv)
  29. Monica Musso; Juncheng Wei, Shusen Yan, Infinitely many positive solutions for a nonlinear field equation with super-critical growth. Proc. Lond. Math. Soc. (3) 112 (2016), no. 1, 1–26.
  30. Monica Musso, Angela Pistoia, Juncheng Wei, New blow-up phenomena for SU(n+1) Toda system. J. Differential Equations 260 (2016), no. 7, 6232–6266. (arxiv)
  31. Monica Musso, Juncheng Wei, Sign-changing blowing-up solutions for supercritical Bahri-Coron’s problem. Calc. Var. Partial Differential Equations 55 (2016), no. 1, Art. 1, 39 pp. (arxiv)
  32. Alexander Quaas, Aliang Xia,  Multiple positive solutions for nonlinear critical fractional elliptic equations involving sign-changing weight functions. Z. Angew. Math. Phys. 67 (2016), no. 3, Art. 40, 21 pp. 3
  33. Alexander Quaas, Aliang Xia, A Liouville type theorem for Lane-Emden systems involving the fractional Laplacian. Nonlinearity 29 (2016) 2279-2297.

  1. Abdellaoui, B.; Biroud, K.; Davila, J.; Mahmoudi, F. Nonlinear elliptic problem related to the Hardy inequality with singular term at the boundary. Commun. Contemp. Math. 17 (2015), no. 3, 1450033, 28 pp. pdf
  2. Agudelo, Oscar; del Pino, Manuel; Wei, Juncheng. Solutions with multiple catenoidal ends to the Allen-Cahn equation in R3. J. Math. Pures Appl. (9) 103 (2015), no. 1, 142–218. pdf
  3. Alejo, Miguel A.; Muñoz, Claudio Dynamics of complex-valued modified KdV solitons with applications to the stability of breathers. Anal. PDE 8 (2015), no. 3, 629–674.
  4. Chen, Huyuan; Felmer, Patricio; Quaas, Alexander; Self-generated interior blow-up solutions of fractional elliptic equation with absorption. Differential Integral Equations 28 (2015), no. 9-10, 839–860. pdf
  5. Chen, Wenjing; Guerra, Ignacio. Multiplicity of solutions to nearly critical elliptic equation in the bounded domain of R3. J. Math. Anal. Appl. 424 (2015), no. 1, 179–200. pdf
  6. Dávila, Juan; Pistoia, Angela; Vaira, Giusi. Bubbling solutions for supercritical problems on manifolds. J. Math. Pures Appl. (9) 103 (2015), no. 6, 1410–1440. pdf
  7. del Pino, Manuel; Wei, Juncheng; Yao, Wei. Intermediate reduction method and infinitely many positive solutions of nonlinear Schrödinger equations with non-symmetric potentials. Calc. Var. Partial Differential Equations 53 (2015). no. 1-2. 473-523. pdf
  8. Deng, Shengbing; Garrido, Danilo; Musso, Monica. Multiple blow-up solutions for an exponential nonlinearity with potential in R2. Nonlinear Anal. 119 (2015), 419–442. pdf
  9. Deng, Shengbing; Musso, Monica Critical points of the Trudinger-Moser trace functional with high energy levels. Ann. Inst. H. Poincaré Anal. Non Linéaire 32 (2015), no. 1, 59–95. pdf
  10. Henao, Duvan; Mora, Carlos; Xu, Xiaoqian. Gamma-convergence approximation of fracture and cavitation in nonlinear elasticity (with C. Mora-Corral & X. Xu), Arch. Ration. Mech. Anal. 216 (2015) 813–879.
  11. Henao, Duvan; Mora-Corral, Carlos; Xu, Xianmin. A numerical study of void coalescence and fracture in nonlinear elasticity. Computer Methods in Applied Mechanics and Engineering. 303. (2016), Pages 163–184 pdf
  12. M.M. Fall, F. Mahmoudi, and E. Valdinocci, Ground states and concentration phenomena for the fractional Shrödinger equation, Nonlinearity 28 (2015), no. 6, 1937–1961. (arxiv)
  13. Mahmoudi, Fethi; Sánchez, Felipe Subiabre; Yao, Wei. On the Ambrosetti-Malchiodi-Ni conjecture for general submanifolds. J. Differential Equations 258 (2015), no. 2, 243–280. pdf
  14. Quaas, Alexander; Xia, Aliang. Liouville type theorems for nonlinear elliptic equations and systems involving fractional Laplacian in the half space. Calc. Var. Partial Differential Equations 52 (2015), no. 3-4, 641–659. pdf
  15. Henao, Duvan; C. Mora-Corral, Regularity of inverses of Sobolev deformations with finite surface energy, J. Funct. Anal. 268 (2015) 2356–2378.
  16. Chen, HY; Felmer, P;Quaas, A, Self-Generated Interior Blow-Up Solutions Of Fractional Elliptic Equation With Absorption, Differential And Integral Equations (2015). pdf
  17. Felmer, P; Torres, C Non-linear Schrodinger equation with non-local regional diffusion, Calculus Of Variations And Partial Differential Equations Scopus (2015). pdf
  18. Felmer, P; Vergara, I, Scalar field equation with non-local diffusion, Nodea-Nonlinear Differential Equations and Applications (2015). pdf
  19. Chen, HY; Felmer, P;Quaas, A, Large solutions to elliptic equations involving fractional Laplacian, Annales De L Institut Henri Poincare- Analyse Non Lineaire (2015). pdf

  1. M.A. Alejo, C. Muñoz, Almost sharp nonlinear scattering in one-dimensional Born-Infeld equations arising in nonlinear Electrodynamics, preprint (arxiv).
  2. M. Cavalcante, C. Muñoz, Stability of KdV solitons on the half-line,  preprint (arxiv).
  3. Huyuan Chen, Alexander Quaas, Classification of isolated singularities of nonnegative solutions to fractional semi-linear elliptic equations and the existence results. (arxiv)
  4. Carmen Cortázar, Manuel del Pino, Monica Musso, Green’s function and infinite-time bubbling in the critical nonlinear heat equation. (arxiv)
  5. Juan Davila, Manuel del Pino, Juncheng Wei, Singularity formation for the two-dimensional harmonic map flow into S^2. (arxiv)
  6. Duván Henao, Carlos Mora-Corral, Xianmin Xu, A numerical study of void coalescence and fracture in nonlinear elasticity. pdf
  7. Anna Kazeykina, Claudio Muñoz, Dispersive estimates for rational symbols and local well-posedness of the nonzero energy NV equation. II., (arxiv).
  8. Claudio Muñoz, Well-posedness for modulationally unstable nonlinear Schrödinger equations, and applications, (arxiv).
  9. C. Muñoz, F. Poblete and J.C. Pozo, Scattering in the energy space for Boussinesq equations,  preprint (arxiv).
  10. Alexander Quaas, Andrei Rodríguez, Loss of boundary conditions for fully nonlinear parabolic equations with superquadratic gradient terms. (arxiv)
  11. Alexander Quaas, Ariel Salort, Aliang Xia, Principal eigenvalues of fully nonlinear integro-differential elliptic equations with a drift term. (arxiv)
  12. Alexander Quaas, Aliang Xia, Existence and uniqueness of positive solutions for a class of logistic type elliptic equations in R^N involving fractional Laplacian. (arxiv)
  13. Alexander Quaas, Aliang Xia, Existence results of positive solutions for nonlinear cooperative elliptic systems involving fractional Laplacian. (arxiv)

  1. del Pino, Manuel; Gkikas, Konstantinos T.;  Ancient shrinking spherical interfaces in the Allen–Cahn flow. Ann. Inst. H. Poincaré Anal. Non Linéaire 35 (2018), no. 1, 187–215.
  2. Shenbing Deng, Zied Khemiri, Fethi Mahmoudi, On spike solutions for a singular perturbed problem on compact Riemannian manifolds. CPAA to appear.
  3. Rupert Frank, Phan Tành Nam, Hanne Van Den Bosch, The ionization conjecture in Thomas-Fermi-Dirac-von Weizsäcker theory, accepted in Communications in Pure and Applied Mathematics.
  4. Kim, Seunghyeok; Musso, Monica; Wei, Juncheng Existence theorems of the fractional Yamabe problem. Anal. PDE 11 (2018), no. 1, 75–113.
  5. Quaas, Alexander; Rodríguez, Andrei;  Loss of boundary conditions for fully nonlinear parabolic equations with superquadratic gradient terms. J. Differential Equations 264 (2018), no. 4, 2897–2935.