Existence results for nonlinear elliptic problems

Abstract

The existence of non-trivial solutions for nonlinear Dirichlet problems involving the p-Laplacian is investigated. In particular, an existence result of at least one non-trivial solution, without requiring any asymptotic condition on the nonlinear term either at zero or at infinity, is presented. As a consequence, also a multiplicity result is pointed out. The approach is based on a local minimum theorem for differentiable functionals.

Keywords:

• Dirichlet problem
• positive solutions
• critical points

AMS Subject Classifications::

• 35J20
• 35J60
• 35J91