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