Strongly nonlinear elliptic variational unilateral problems in Orlicz space

Abstract

We will be concerned with the existence result of unilateral problem associated to the equations of the form Au+g(x,u,∇u)=f, where A is a Leray-Lions operator from its domain D(A)⊂W01LM(Ω) into W−1EM¯(Ω). On the nonlinear lower order term g(x,u,∇u), we assume that it is a Carathéodory function having natural growth with respect to |∇u|, and satisfies the sign condition. The right-hand side f belongs to W−1EM¯(Ω).