Multiple solutions for a class of quasilinear elliptic equations of p(x)-Laplacian type with nonlinear boundary conditions

Abstract

Using variational methods we study the non-existence and multiplicity of non-negative solutions for a class of quasilinear elliptic equations of p(x)-Laplacian type with nonlinear boundary conditions of the formwhere Ω; is a bounded domain with smooth boundary, n is the outer unit normal to ∂Ω and λ is a parameter. Furthermore, we want to emphasize that g : ∂Ω × [0,∞)→ ℝ is a continuous function that may or may not satisfy the Ambrosetti–Rabinowitz-type condition.