Infinitely many solutions for a class of nonlinear eigenvalue problem in Orlicz-Sobolev spaces

We study the Neumann problem - div(alpha(vertical bar del u vertical bar)del u) + alpha(vertical bar u vertical bar)u = lambda f (x, u) in Omega, partial derivative u/partial derivative v = 0 on partial derivative Omega, where Omega is a smooth bounded domain in R(N), lambda is a positive parameter, f is a continuous function, and alpha is a real-valued mapping defined on (0, infinity). The main result in this Note establishes that for all lambda in a prescribed open interval, this problem has infinitely many solutions that converge to zero in the Orlicz-Sobolev space W(1)L(Phi)(Omega).