Nonlinear Analysis of PDE
The Nonlinear Analysis is one of the areas of Mathematics that has presented greater growth in the last years due to the fact that the methods developed there are adaptable to many others areas of Mathematics and to different types of Partial Differential Equations. These methods constitute a powerful tool to understand and to solve diverse problems coming from models in Biology, Finance and Control Theory.
Our group has special interest in studying fully nonlinear local and nonlocal elliptic and parabolic equations, which does not prevent us from dealing with problems that involve only the Laplace operator.
We are interested in proving existence and obtaining qualitative properties of the solutions for these types of equations. We have also a special interest in understanding the complexity of the solution sets that these equations sometimes hide. Notice that most of the qualitative properties and the structure of the solution sets that we are searching for will give rise to different interpretations from the theoretical and the applied point of views.
- 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]
- 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]
- 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]
- Tan J, Ying W, Jianfu Y. Nonlinear fractional field equations. Nonlinear Anal. 2012;75(4):2098–2110. [Bibtex]
- 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]
- FONDECYT 1120842: Multiplicity of solutions for quasilinear and non-local elliptic problems
- FONDECYT Nº 1090518: Radial Solutions of Semilinear Elliptic Problems: A Geometric Approach
- FONDECYT Nº 1050968: Geometry of Phase Space and Radial Solutions of NonlInear Elliptic Problems
- FONDECYT-Postdoctorado Nº 3010044: Geometry of Phase Space and Radial Solutions of Nonlinear Elliptic Problems
- FONDECYT 3060061: Generalized quasilinear elliptic equations with singular weights.