Strongly nonlinear elliptic problem with measure data in Musielak-Orlicz spaces

Abstract

ABSTRACT In this paper, we investigate the existence theorem of entropy solutions for nonlinear elliptic problem of the type in Ω, in the setting of Musielak-Orlicz spaces. The lower order term Φ verifies the natural growth condition, the nonlinearity g has a natural growth with respect to its third argument and with sign condition, no -condition is assumed on the Musielak function, and the datum μ is assumed to belong to .