Existence and multiplicity of solutions for non-degenerate Kirchhoff type problem with nonlinear boundary condition

Abstract

We show the existence of solutions for nonlinear elliptic partial differential equations with Steklov nonlinear boundary conditions involving a Kirchhoff type operator. By using variational and topological methods, we prove the existence and multiplicity of solutions. The results obtained are new even for the standard stationary Kirchhoff equation with nonlinear boundary condition involving the p-Laplacian operator.

Keywords

• Variational methods
• nonlinear elliptic equations
• Steklov-Neumann eigenvalues