## Differential and Integral Equations

### Multiple nontrivial solutions for $p$-Laplacian equations with an asymmetric nonlinearity

#### Abstract

In this paper we study a nonlinear Dirichlet problem driven by the p-Laplacian and a right-hand side nonlinearity which exhibits an asymmetric behavior near $+ \infty$ and $- \infty$. Using variational techniques based on the mountain pass theorem and the second deformation theorem, we prove the existence of at least two nontrivial $C^1$- solutions, one of which is strictly positive.

#### Article information

Source
Differential Integral Equations, Volume 19, Number 12 (2006), 1371-1390.

Dates
First available in Project Euclid: 21 December 2012

Hu, Shouchuan; Papageorgiou, Nikolaos S. Multiple nontrivial solutions for $p$-Laplacian equations with an asymmetric nonlinearity. Differential Integral Equations 19 (2006), no. 12, 1371--1390. https://projecteuclid.org/euclid.die/1356050294