An existence result for three solutions to a Dirichlet problem with real parameter

Abstract

In this article, we establish the existence of solutions for partial differential equations (PDE) with boundary value conditions. For studying the existence result, suppose that some condition to find at least three nontrivial solutions for Dirichlet doubly eigenvalue boundary value problem by using Theorem of three-critical points.

Subject Classification:

• Primary 93A30
• Secondary 49K15

Keywords:

• Dirichlet problem
• Partial differential equations
• Existence solutions
• Critical points method