Lagrange Multiplier Rule to a Nonlinear Eigenvalue Problem in Musielak-Orlicz Spaces

摘要

In this paper, we shall be concerned with the existence result of the following eigenvalue problemin an arbitrary Musielak-Orlicz Spaces, with an indefinite bounded weight rho which changes sign, and such that We show that the existence of an eigenvalue can be derived from a generalized version of Lagrange multiplier rule without assuming any restriction on generalized N-function M.