Alexander Quaas

Email     email
Phone     (56 32) 2654489
Office     F 238 (Casa Central, Valparaiso)
Research area     Nonlinear Analysis of PDE
Personal page        
Alexander Quaas
 
Publications:
  1. Quaas A, Xia A. A Liouville type theorem for Lane–Emden systems involving the fractional Laplacian. Nonlinearity 2016;29(8):2279.  [Digital version]  [Bibtex]
  2. Quaas A, Xia A. Multiple positive solutions for nonlinear critical fractional elliptic equations involving sign-changing weight functions. Zeitschrift f{"u}r angewandte Mathematik und Physik 2016;67(3):1-21.  [Digital version]  [Bibtex]
  3. Alarcón S, Burgos-Pérez M. Á, García-Melián J, Quaas A. Nonexistence results for elliptic equations with gradient terms. Journal of Differential Equations 2016;260:758-780. [Bibtex]
  4. Quaas A, Burgos-Pérez M. Á, García-Melián J. Classification of supersolutions and Liouville theorems for some nonlinear elliptic problems. Discrete and Continuous Dynamical Systems 2016;36(9):4703-4721.  [Digital version]  [Bibtex]
  5. Quaas A, García-Melián J, Sirakov B. Elliptic equations with absorption in a half-space. Bulletin of the Brazilian Mathematical Society, New Series 2016:1-11.  [Digital version]  [Bibtex]
  6. Quaas A, García-Melián J, Alarcón S. Optimal Liouville theorems for supersolutions of elliptic equations with the Laplacian. Annali della Scuola Normale Superiore di Pisa. Classe di scienze 2016;16(1):129-158.  [Digital version]  [Bibtex]
  7. Quaas A, Xia A. Liouville type theorems for nonlinear elliptic equations and systems involving fractional Laplacian in the half space. Calculus of Variations and Partial Differential Equations 2015;52(3-4):641-659.  [Digital version]  [Bibtex]
  8. Quaas A, Chen H, Felmer P. Self-generated interior blow-up solutions of fractional elliptic equation with absorption. Differential and Integral Equations 2015;28(9-10):839-860.  [Digital version]  [Bibtex]
  9. Chen H, Felmer P, Quaas A. Large solutions to elliptic equations involving fractional Laplacian. Ann. Inst. Henri Poincare, Analyse non lineaire 2015;32(6):1199-1228.  [Digital version]  [Bibtex]
  10. Alarcón S, García-Melián J, Quaas A. Existence and non-existence of solutions to elliptic equations with a general convection term. Proc. Roy. Soc. Edinburgh Sect. A 2014;144:225-239. [Bibtex]
  11. Alarcón S, Quaas A, García-Melián J. Nonexistence of positive supersolutions to some nonlinear elliptic problems. J. Math. Pures Appl. 2013;99:618-634. [Bibtex]
  12. Alarcón S, Quaas A. Large viscosity solutions for some fully nonlinear equations. NoDEA Nonlinear Differential Equations Appl. 2013;20:1453-1472. [Bibtex]
  13. Quaas A, Felmer P, Sirakov B. Solvability of nonlinear elliptic equations with gradient terms.. J. Differential Equations 2013;254(11):4327–4346. [Bibtex]
  14. Quaas A, Alarcón S, Garcia-Mellian J. Liouville type theorems for elliptic equations with gradient terms.. Milan J. Math. 2013;81(1):171–185. [Bibtex]
  15. Alarcón S, Quaas A, García-Melián J. Keller-Osserman type conditions for some elliptic problems with gradient terms. Journal of Differential Equations 2012;252:886–914. [Bibtex]
  16. Alarcón S, Quaas A, Iturriaga L. Existence and multiplicity results for Pucci's operators involving nonlinearities with zeros. Cal. Var. 2012;45:443-454. [Bibtex]
  17. Alarcón S, Quaas A, García-Melián J. Existence and uniqueness of solutions to nonlinear elliptic equations without growth conditions at infinity. J. Anal. Math. 2012;118:83-104. [Bibtex]
  18. Quaas A, Tan J, Felmer P. Positive solutions of the nonlinear Schrödinger equation with the fractional Laplacian.. Proc. Roy. Soc. Edinburgh Sect. A 2012;142(6). [Bibtex]
  19. Quaas A, Meneses R. Existence and non-existence of global solutions for uniformly parabolic equations. J. Evol. Equ. 2012;12(4):943–955. [Bibtex]
  20. Quaas A, Felmer P. Boundary blow up solutions for fractional elliptic equations.. Asymptot. Anal. 2012;78(3):123–144. [Bibtex]
  21. Quaas A, Felmer P, Sirakov B. Existence and regularity results for fully nonlinear equations with singularities.. Math. Ann. 2012;354(1):377–400. [Bibtex]
  22. Felmer P, Quaas A. Fundamental solutions and Liouville type theorems for nonlinear integral operators. Advances in Mathematics 2011;226(3):2712-2738.  [Digital version]  [Bibtex]
  23. Meneses R, Quaas A. Fujita type exponent for fully nonlinear parabolic equations and existence results. Journal of Mathematical Analysis and Applications 2011;376(2):514-527.  [Digital version]  [Bibtex]
  24. Allendes A, Quaas A. Multiplicity results for extremal operators through bifurcation. Discrete Continuous Dynamical Systems 2011;29(1):51-65.  [Digital version]  [Bibtex]
  25. Quaas A, Felmer P. Fundamental solutions for a class of Isaacs integral operators.. Discrete Contin. Dyn. Syst. 2011;30(2):493–508. [Bibtex]
  26. Quaas A, Felmer P, Sirakov B. Landesman-Lazer type results for second order Hamilton-Jacobi-Bellman equations. Journal of Functional Analysis 2010;258:4154-4182. [Bibtex]
  27. Esteban M, Felmer P, Quaas A. Eigenvalues for Radially Symmetric Fully Nonlinear Operators. Communications in Partial Differential Equations 2010;35(9):1716 - 1737.  [Digital version]  [Bibtex]
  28. Davila G, Felmer P, Quaas A. Harnack inequality for singular fully nonlinear operators and some existence results. Calculus o Variations and PDE 2010;39(3-4):557-578.  [Digital version]  [Bibtex]
  29. Felmer P, Quaas A, Sirakov B. Resonance phenomena for second-order stochastic control equations. SIAM J. on Mathematical Analysis 2010;42(3):997-1024.  [Digital version]  [Bibtex]
  30. Felmer P, Quaas A, Tan J. Geometry of phase plane and radial solutions for nonlinear elliptic equations with extremal operators. Journal Mathematical Analisys Aplication 2010;366(1):101-111.  [Digital version]  [Bibtex]
  31. Alarcón S, Quaas A. Large number of fast decay ground states to Matukuma-type equations. Journal of Differential Equations 2010;248:866-892.  [Digital version]  [Bibtex]
  32. Esteban M, Felmer P, Quaas A. Super-linear elliptic equation for fully nonlinear operators without growth restrictions for the data. Proc. Roy. Soc. Edinburgh 2010;53:125-141.  [Digital version]  [Bibtex]
  33. Davila G, Felmer P, Quaas A. Alexandroff-Bakelman-Pucci estimate for singular or degenerate fully nonlinear elliptic equations. Comptes Rendus Mathematique, 2009;347(19-20):1165-1168.  [Digital version]  [Bibtex]
  34. Quaas A, Felmer P, Tang M, Yu J. Random dynamics of gene transcription activation in single cells. Journal of Differential Equations 2009;247(6):1796-1816.  [Digital version]  [Bibtex]
  35. Felmer P, Montenegro M, Quaas A. A note on the Strong Maximum Principle and the Compact Support Principle. Journal of Diff. Equation 2009;246(1):39-49.  [Digital version]  [Bibtex]
  36. Quaas A, Sirakov B. Existence and non-existence results for fully nonlinear elliptic systems. ndiana Univ. Math Journal 2009;58(2).  [Digital version]  [Bibtex]
  37. Felmer P, Quaas A, Tang M. On the complex structure of positive solutions to Matukuma-type equations. Ann. Inst. Henri Poincare, Analyse non lineaire 2009;26(3):869-887.  [Digital version]  [Bibtex]
  38. Felmer P, Quaas A. Fundamental solutions and two properties of elliptic maximal and minimal operators. Transactions of the American Mathematical Society 2009;361:5721-5736.  [Digital version]  [Bibtex]
  39. Quaas A, Sirakov B. Solvability of monotone systems of fully nonlinear elliptic PDE´s. omptes Rendus Mathematique 2008;346(11-12):641-644.  [Digital version]  [Bibtex]
  40. Felmer P, Quaas A, Tang M, Yu J. Monotonicity properties for ground states of the scalar field equation. Ann. Inst. Henri Poincare, Analyse non lineaire 2008;25(1):105-119.  [Digital version]  [Bibtex]
  41. Quaas A, Sirakov B. Principal eigenvalues and the Dirichlet problem for fully nonlinear operators. Adv. in Mathematics 2008;218(1):105-135.  [Digital version]  [Bibtex]
  42. Esteban M, Felmer P, Quaas A. Large critical exponents for some second order uniformly elliptic operators. Communications in Partial Differential Equations 2007;32(4):543 - 556.  [Digital version]  [Bibtex]
  43. Quaas A, Sirakov B. On the principal eigenvalues and the Dirichlet problem for fully nonlinear operators. Comptes Rendus Mathematique 2006;342(2):115-118. [Bibtex]
  44. Felmer P, Quaas A. Critical exponents for uniformly elliptic extremal operators. Indiana Univ. Math Journal 2006;55(2):593-629.  [Digital version]  [Bibtex]
  45. Felmer P, Quaas A, Tang M. On uniqueness for nonlinear elliptic equation involving the Pucci´s extremal operator. Journal of Diff. Equation 2006;226(1):80-98.  [Digital version]  [Bibtex]
  46. Quaas A, Sirakov B. Existence results for nonproper elliptic equation involving the Pucci´s Operator. Communications in Partial Differential Equations 2006;31(7):987 - 1003.  [Digital version]  [Bibtex]
  47. Busca J, Esteban M, Quaas A. Nonlinear Eigenvalues and Bifurcation problems for Pucci´s Operator. Ann. Inst. Henri Poincare, Analyse non lineaire 2005;22(2):187-206. [Bibtex]
  48. Felmer P, Quaas A. Positive Radial Solutions to a ´semilinear´ equation involving the Pucci´s operator. J. Differential Equation 2004;199(2):376-393. [Bibtex]
  49. Quaas A. Existence of Positive Solutions to a ´semilinear´ equation involving the Pucci´s operator in a convex domain. Differential Integral Equation 2004;17(5-6):481-494. [Bibtex]
  50. Felmer P, Quaas A. On Critical Exponents for Pucci´s Extremal Operators. Ann. Inst. Henri Poincare, Analyse non lineaire 2003;20(5):843-865. [Bibtex]
  51. Busca J, Quaas A. Qualitative Properties for Semilinear Elliptic Systems with Non-Lipschitz Nonlinearity. Nonlinear Analysis TMA 2002;50(3):299-312. [Bibtex]
  52. Felmer P, Quaas A. On The Strong Maximum Principle for Quasilinear Elliptic Equations and Systems. Adv. in Differential Equation 2002;7:25-46. [Bibtex]
  53. Felmer P, Quaas A. Critical Exponents for Pucci´s Extremal Operators. C.R. Acad. Sci. Paris (I) 2002;335:909-914. [Bibtex]
        
Projects:
  1. FONDECYT 1151180: Some Nonlinear local and non-local equations
  2. Millennium Nucleus Center for Analysis of PDE, NC130017
  3. CONCURSO “ATRACCIÓN DE CAPITAL HUMANO AVANZADO DEL EXTRANJERO” - Modalidad Estadías Cortas (MEC) –Consolidación de la línea de EDP's en el Doctorado Regional en Matemática
  4. Mathamsud 13MATH-03 - QUESP - Quasilinear Equations and Singular Problems
  5. Ministerio de Ciencia e Innovación - Ministerio de Economía y Competitividad (Gobierno de España) MTM2011-27998 "Propiedades cualitativas de ecuaciones y sistemas elípticos no lineales: difusión local y no local"
 
 
 
 
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