A Multiplicity Result for a Class of Quasilinear Elliptic and Parabolic Problems
Date
1997-04-22
Authors
Grossinho, Maria do Rosario
Omari, Pierpaolo
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
Abstract
We prove the existence of infinitely many solutions for a class of quasilinear elliptic and parabolic equations, subject respectively to Dirichlet and Dirichlet-periodic boundary conditions. We assume that the primitive of the nonlinearity at the right-hand side oscillates at infinity. The proof is based on the construction of upper and lower solutions, which are obtained as solutions of suitable comparison equations. This method allows the introduction of conditions on the potential for the study of parabolic problems, as well as to treat simultaneously the singular and the degenerate case.
Description
Keywords
Quasilinear, Elliptic, Parabolic problems
Citation
Grossinho, M., & Omari, P. (1997). A multiplicity result for a class of quasilinear elliptic and parabolic problems. <i>Electronic Journal of Differential Equations, 1997</i>(08), pp. 1-16.
Rights
Attribution 4.0 International