Existence and multiplicity of solutions for semilinear elliptic equations with Neumann boundary conditions

Abstract

This article shows the existence of solutions by the least action principle, for semilinear elliptic equations with Neumann boundary conditions, under critical growth and local coercive conditions. In the subcritical growth and local coercive case, multiplicity results are established by using the minimax methods together with a standard eigenspace decomposition.

Keywords

• Elliptic equations
• Neumann boundary conditions
• critical point
• least action principle
• minimax methods