Variational inequalities with multivalued lower order terms and convex functionals in orlicz-sobolev spaces

We consider the existence of solutions of variational inequality form. find u ε d (j): 〈 a (u),v - u 〉 + 〈 f (u),v - u 〉 + j (v) - j (u) ≥ 0,∀ v ε w 1 l m (ω),whose principal part is having a growth not necessarily of polynomial type,where a is a second-order elliptic operator of leray-lions type,f is a multivalued lower order term,and j is a convex functional. we use subsupersolution methods to study the existence and enclosure of solutions in orlicz-sobolev spaces. © 2015 ge dong and xiaochun fang.