Existence and multiplicity of solutions for nonlinear elliptic Dirichlet systems

Abstract

The existence and multiplicity of solutions for systems of nonlinear elliptic equations with Dirichlet boundary conditions is investigated. Under suitable assumptions on the potential of the nonlinearity, the existence of one, two, or three solutions is established. Our approach is based on variational methods.

Keywords

• Elliptic systems
• variational problems
• multiple solutions