Nonlinear elliptic equations with divergence term and without sign condition

Abstract

This paper aims at bounded solutions for nonlinear Dirichlet problems with divergence term in a bounded domains. Our results is obtained without imposing any sign condition on the term which growth quadratically to the gradient. For a given source term in a suitable Lebesgue spaces and with less regularity on the divergence term, We establish an existence and regularity results of solutions. Our approach falls within the scope of Schauder fixed point theorem, some properties of a priori estimates and Stampacchia's L1-regularity.