NONLINEAR ELLIPTIC EQUATIONS WITH MEASURE DATA IN ORLICZ SPACES

We study the existence result for a unilateral problem Au - div(Phi(x, u)) + H(x, u, del u) = mu, where Au = -div(a(x, u, del u)) is a Leray-Lions operator defined in the Sobolev-Orlicz space D(A) subset of W-0(1) L-M (Omega) , mu is an element of L-1 (Omega) W-1 E-(M) over bar(Omega), where M and (M) over bar are two complementary N-functions. The first and second lower terms Phi and H satisfy solely the growth condition and an arbitrary sign condition and, moreover, u >= zeta, where zeta is a measurable function.