Arbitrarily small weak solutions for a nonlinear eigenvalue problem in Orlicz–Sobolev spaces

Abstract

Under an appropriate oscillating behavior of the nonlinear term, the existence of a determined open interval of positive parameters for which an eigenvalue non-homogeneous Neumann problem admits infinitely many weak solutions that strongly converges to zero, in an appropriate Orlicz–Sobolev space, is proved. Our approach is based on variational methods. The abstract result of this paper is illustrated by a concrete case.