Electron. J. Diff. Eqns., Vol. 1997(1997), No. 08, pp 1-16.

A Multiplicity Result for a Class of Quasilinear Elliptic and Parabolic Problems

Maria do Rosario Grossinho & Pierpaolo Omari

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.

Submitted January 10, 1997. Published April 22, 1997.
Math Subject Classification: 35J65, 35J70, 35K60, 35K65.
Key Words: Quasilinear, Elliptic, Parabolic Problems.

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Maria do Rosario Grossinho
Centro de Matematica e Aplicacoes Fundamentais, Universidade de Lisboa, Av. Prof. Gama Pinto 2, 1699 Lisboa Codex, Portugal
e-mail: mrg@ptmat.lmc.fc.ul.pt

Pierpaolo Omari
Dipartimento di Scienze Matematiche, Universita di Trieste, Piazzale Europa 1, I-34127, Trieste, Italia
e-mail: omari@univ.trieste.it

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