# Wydawnictwa / Czasopisma IMPAN / Colloquium Mathematicum / Wszystkie zeszyty

## Multiple solutions for nonlinear discontinuous elliptic problems near resonance

### Tom 81 / 1999

Colloquium Mathematicum 81 (1999), 89-99 DOI: 10.4064/cm-81-1-89-99

#### Streszczenie

We consider a quasilinear elliptic eigenvalue problem with a discontinuous right hand side. To be able to have an existence theory, we pass to a multivalued problem (elliptic inclusion). Using a variational approach based on the critical point theory for locally Lipschitz functions, we show that we have at least three nontrivial solutions when $λ → λ_1$ from the left, $λ_1$ being the principal eigenvalue of the p-Laplacian with the Dirichlet boundary conditions.

#### Autorzy

• Nikolaos Kourogenis
• Nikolaos Papageorgiou

## Przeszukaj wydawnictwa IMPAN

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Odśwież obrazek