Alexander-Quass

Alexander Quaas

PHD en Matematics, Universidad de Chile & Université de Paris Dauphine, France (2003)
Civil Engineering in Mathematics, Universidad de Chile  (1999).

Position: Full Professor

Institution:  Universidad Técnica Fedederico Santa María

Research area: Nonlinear Analysis.

Contact:

Emailalexander.quaas@usm.cl

Phone: +56 32 265 4489

Adress: España 1680, Casilla 110, Valparaíso, Chile.

Publications

  • B. Barrios, L. Del Pezzo, J. García-Melián, A. Quaas, A priori bounds and existence of solutions for some nonlocal elliptic problems, to appear in Rev. Iberoamericana.
  • Quaas, E. Topp, Existence and Uniqueness of Large Solutions for a Class of Non Uni- formly Elliptic Semilinear Equations, to appear in Journal d’Analyse Math.
  • 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.
  • Gonzalo Davila, Erwin Topp; Alexander Quaas, Continuous viscosity solutions  nonlocal Dirichlet problems with coercive gradient terms. Math. Ann. DOI 10.1007/s00208-016-1481-3
  • S. Alarcón, M. Burgos-Pérez, J. García-Melián, A. Quaas, Nonexistence results for elliptic equations with gradient terms, Journal of Differential Equations 260 (2016), no. 1, 758-780.
  • S. Alarcón, J. García-Melian, A. Quaas, Optimal Liouville Theorems for supersolution of elliptic equation with the Laplacian, Annali della Scuola
    Normale Superiore di Pisa Cl. Sci. (5) Vol. XVI (2016), 129-158.
  • A. Quaas, A, Xia, Multiple positive solutions for nonlinear critical fractional elliptic equations involving sign-changing weight functions,
    Zeitschrift fuer Angewandte Mathematik und Physik (2016) 67:40 2016 .
  • A. Quaas, A, Xia, A Liouville type theorem for Lane-Emden systems involving the fractional Laplacian, Nonlinearity 29 (2016) 2279-2297.
  • S. Alarcón, M. Burgos-Pérez, J. García-Melián, A. Quaas, 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 .
  • J. García-Melián, Alexander Quaas, Boyan Sirakov, Elliptic Equation with absorption in the half space, Bull Braz Math Soc, New Series 47(3),
    811-821.
  • L .Del Pezzo; A. Quaas, Global Bifurcation for Fractional p-Laplacian and an Application. Z. Anal. Anwend. 35 (2016), no. 4, 411–447.
  •  H. Chen, P.  Felmer, A. Quaas, Large solutions to elliptic equations involving fractional Laplacian, Ann. Inst. Henri Poincare, Analyse non
    lineaire, Volume 32, Issue 6, November–December 2015.
  • 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
  • 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
  • Alarcón, Salomón; García-Melián, Jorge; Quaas, Alexander. Existence and non-existence of solutions to elliptic equations with a general convection term. Proc. Roy. Soc. Edinburgh Sect. A 144 (2014), no. 2, 225–239. pdf
  • Alarcón, S.; Quaas, A. Large viscosity solutions for some fully nonlinear equations.NoDEA Nonlinear Differential Equations Appl. 20 (2013), no. 4, 1453–1472. pdf
  • Alarcón, Salomón; García-Melián, Jorge; Quaas, Alexander Liouville type theorems for elliptic equations with gradient terms. Milan J. Math. 81 (2013), no. 1, 171–185. pdf
  • Alarcón, S.; García-Melián, J.; Quaas, A. Nonexistence of positive supersolutions to some nonlinear elliptic problems. J. Math. Pures Appl. (9) 99 (2013), no. 5, 618–634. pdf
  • Felmer, Patricio; Quaas, Alexander; Sirakov, Boyan Solvability of nonlinear elliptic equations with gradient terms. J. Differential Equations 254 (2013), no. 11, 4327–4346. pdf
  • Felmer, Patricio; Quaas, Alexander; Tan, Jinggang. Positive solutions of the nonlinear Schrödinger equation with the fractional Laplacian. Proc. Roy. Soc. Edinburgh Sect. A142 (2012), no. 6, 1237–1262. pdf
  • Meneses, Rodrigo; Quaas, Alexander. Existence and non-existence of global solutions for uniformly parabolic equations. J. Evol. Equ. 12 (2012), no. 4, 943–955. pdf
  • Alarcón, Salomón; García-Melián, Jorge; Quaas, Alexander. Existence and uniqueness of solutions of nonlinear elliptic equations without growth conditions at infinity. J. Anal. Math. 118 (2012), no. 1, 83–104. pdf
  • Alarcón, Salomón; Iturriaga, Leonelo; Quaas, Alexander Existence and multiplicity results for Pucci’s operators involving nonlinearities with zeros. Calc. Var. Partial Differential Equations 45 (2012), no. 3-4, 443–454. pdf
  • Felmer, Patricio; Quaas, Alexander. Boundary blow up solutions for fractional elliptic equations. Asymptot. Anal. 78 (2012), no. 3, 123–144. pdf
  • Felmer, Patricio; Quaas, Alexander; Sirakov, Boyan Existence and regularity results for fully nonlinear equations with singularities. Math. Ann. 354 (2012), no. 1, 377–400. pdf
  • Alarcón, Salomón; García-Melián, Jorge; Quaas, Alexander. Keller-Osserman type conditions for some elliptic problems with gradient terms. J. Differential Equations252 (2012), no. 2, 886–914. pdf
  • Felmer, Patricio; Quaas, Alexander. Fundamental solutions for a class of Isaacs integral operators. Discrete Contin. Dyn. Syst. 30 (2011), no. 2, 493–508. pdf
  • Meneses, Rodrigo; Quaas, Alexander Fujita type exponent for fully nonlinear parabolic equations and existence results. J. Math. Anal. Appl. 376 (2011), no. 2, 514–527. pdf
  • Felmer, Patricio; Quaas, Alexander. Fundamental solutions and Liouville type theorems for nonlinear integral operators. Adv. Math. 226 (2011), no. 3, 2712–2738. pdf
  • Allendes, Alejandro; Quaas, Alexander. Multiplicity results for extremal operators through bifurcation. Discrete Contin. Dyn. Syst. 29 (2011), no. 1, 51–65. pdf
  • Esteban, Maria J.; Felmer, Patricio; Quaas, Alexander. Eigenvalues for radially symmetric fully nonlinear operators. Comm. Partial Differential Equations 35 (2010), no. 9, 1716–1737. pdf
  • Dávila, Gonzalo; Felmer, Patricio; Quaas, Alexander. Harnack inequality for singular fully nonlinear operators and some existence results. Calc. Var. Partial Differential Equations 39 (2010), no. 3-4, 557–578. pdf
  • Felmer, Patricio; Quaas, Alexander; Sirakov, Boyan. Resonance phenomena for second-order stochastic control equations. SIAM J. Math. Anal. 42 (2010), no. 3, 997–1024. pdf
  • Felmer, Patricio; Quaas, Alexander; Sirakov, Boyan. Landesman-Lazer type results for second order Hamilton-Jacobi-Bellman equations. J. Funct. Anal. 258 (2010), no. 12, 4154–4182. pdf
  • Felmer, Patricio; Quaas, Alexander; Tan, Jinggang. Geometry of phase plane and radial solutions for nonlinear elliptic equations with extremal operators. J. Math. Anal. Appl. 366 (2010), no. 1, 101–111. pdf
  • Esteban, Maria J.; Felmer, Patricio L.; Quaas, Alexander Superlinear elliptic equation for fully nonlinear operators without growth restrictions for the data. Proc. Edinb. Math. Soc. (2) 53 (2010), no. 1, 125–141. pdf
  • Alarcón, Salomón; Quaas, Alexander. Large number of fast decay ground states to Matukuma-type equations. J. Differential Equations 248 (2010), no. 4, 866–892. pdf
  • Dávila, Gonzalo; Felmer, Patricio; Quaas, Alexander Alexandroff-Bakelman-Pucci estimate for singular or degenerate fully nonlinear elliptic equations. C. R. Math. Acad. Sci. Paris 347 (2009), no. 19-20, 1165–1168. pdf
  • Felmer, Patricio L.; Quaas, Alexander; Tang, Moxun; Yu, Jianshe Random dynamics of gene transcription activation in single cells. J. Differential Equations 247 (2009), no. 6, 1796–1816. pdf
  • Felmer, Patricio L.; Quaas, Alexander Fundamental solutions and two properties of elliptic maximal and minimal operators. Trans. Amer. Math. Soc. 361 (2009), no. 11, 5721–5736. pdf
  • Felmer, Patricio; Quaas, Alexander; Tang, Moxun On the complex structure of positive solutions to Matukuma-type equations. Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (2009), no. 3, 869–887.pdf
  • Quaas, Alexander; Sirakov, Boyan. Existence and non-existence results for fully nonlinear elliptic systems. Indiana Univ. Math. J. 58 (2009), no. 2, 751–788. pdf
  • Felmer, Patricio; Montenegro, Marcelo; Quaas, Alexander A note on the strong maximum principle and the compact support principle. J. Differential Equations 246 (2009), no. 1, 39–49. pdf
  • Felmer, Patricio; Quaas, Alexander Around viscosity solutions for a class of superlinear second order elliptic differential equations. On the notions of solution to nonlinear elliptic problems: results and developments, 205–228, Quad. Mat., 23, Dept. Math., Seconda Univ. Napoli, Caserta, 2008. pdf
  • Quaas, Alexander; Sirakov, Boyan. Solvability of monotone systems of fully nonlinear elliptic PDE’s. C. R. Math. Acad. Sci. Paris 346 (2008), no. 11-12, 641–644. pdf
  • Quaas, Alexander; Sirakov, Boyan. Principal eigenvalues and the Dirichlet problem for fully nonlinear elliptic operators. Adv. Math. 218 (2008), no. 1, 105–135. pdf
  • Felmer, Patricio L.; Quaas, Alexander; Tang, Moxun; Yu, Jianshe. Monotonicity properties for ground states of the scalar field equation. Ann. Inst. H. Poincaré Anal. Non Linéaire 25 (2008), no. 1, 105–119. pdf
  • Esteban, Maria J.; Felmer, Patricio L.; Quaas, Alexander. Large critical exponents for some second order uniformly elliptic operators. Comm. Partial Differential Equations32 (2007), no. 4-6, 543–556. pdf
  • Quaas, Alexander; Sirakov, Boyan. Existence results for nonproper elliptic equations involving the Pucci operator. Comm. Partial Differential Equations 31 (2006), no. 7-9, 987–1003. pdf
  • Felmer, Patricio L.; Quaas, Alexander; Tang, Moxun. On uniqueness for nonlinear elliptic equation involving the Pucci’s extremal operator. J. Differential Equations 226 (2006), no. 1, 80–98. pdf
  • Felmer, Patricio L.; Quaas, Alexander Critical exponents for uniformly elliptic extremal operators. Indiana Univ. Math. J. 55 (2006), no. 2, 593–629. pdf
  • Quaas, Alexander; Sirakov, Boyan. On the principal eigenvalues and the Dirichlet problem for fully nonlinear operators. C. R. Math. Acad. Sci. Paris 342 (2006), no. 2, 115–118. pdf
  • Felmer, Patricio; Quaas, Alexander Some recent results on equations involving the Pucci’s extremal operators. Contributions to nonlinear analysis, 263–281, Progr. Nonlinear Differential Equations Appl., 66, Birkhäuser, Basel, 2006. pdf
  • Busca, Jérôme; Esteban, Maria J.; Quaas, Alexander. Nonlinear eigenvalues and bifurcation problems for Pucci’s operators. Ann. Inst. H. Poincaré Anal. Non Linéaire22 (2005), no. 2, 187–206. pdf
  • Quaas, Alexander Existence of a positive solution to a “semilinear” equation involving Pucci’s operator in a convex domain. Differential Integral Equations 17 (2004), no. 5-6, 481–494. pdf
  • Felmer, Patricio L.; Quaas, Alexander. Positive radial solutions to a `semilinear’ equation involving the Pucci’s operator. J. Differential Equations 199 (2004), no. 2, 376–393.  pdf
  • Felmer, Patricio L.; Quaas, Alexander On critical exponents for the Pucci’s extremal operators. Ann. Inst. H. Poincaré Anal. Non Linéaire 20 (2003), no. 5, 843–865.
  • Felmer, Patricio L.; Quaas, Alexander. Critical exponents for the Pucci’s extremal operators. C. R. Math. Acad. Sci. Paris 335 (2002), no. 11, 909–914. pdf
  • Busca, Jérôme; Quaas, Alexander Qualitative properties for semilinear elliptic systems with non-Lipschitz nonlinearity. Nonlinear Anal. 50 (2002), no. 3, Ser. A: Theory Methods, 299–312.
  • Felmer, Patricio L.; Quaas, Alexander On the strong maximum principle for quasilinear elliptic equations and systems. Adv. Differential Equations 7 (2002), no. 1, 25–46.