Some results on strongly nonlinear anisotropic differential equations

Abstract

Abstract. The paper concerns the existence of weak solutions to nonlinear elliptic equations of the form A(u) + g(x, u, ∇u) = f, where A is an operator from an appropriate anisotropic function space to its dual and the right hand side term is in L 1+m with 0 < m < 1. We assume a sign condition on the nonlinear term g, but no growth restrictions on u.