A variational approach for mixed elliptic problems involving the p-Laplacian with two parameters

Abstract

Abstract By exploiting an abstract critical-point result for differentiable and parametric functionals, we show the existence of infinitely many weak solutions for nonlinear elliptic equations with nonhomogeneous boundary conditions. More accurately, we determine some intervals of parameters such that the treated problem admits either an unbounded sequence of solutions or a pairwise distinct sequence of solutions that strongly converges to zero. No symmetric condition on the nonlinear term is considered.

Keywords

• Mixed problem
• Critical points
• Weak solutions
• Infinitely many solutions