Existence results to a nonlinear p(x)-Laplace equation with degenerate coercivity and zero-order term: renormalized and entropy solutions

Abstract

This paper is devoted to the study of a nonlinear elliptic equation with degenerate coercivity, zero-order term and L1 datum in the setting of variable exponent Sobolev space. The authors obtain the existence of renormalized solution and entropy solution via strong convergence of truncation. They also get some a priori estimates to the solution and the generalized gradient of the solution in the Marcinkiewicz space with variable exponent.