(untitled) (JOURNAL OF ADVANCES IN MATHEMATICS, 2013)
In this paper, we study the existence of solutions for quasilinear degenerated elliptic operators Au + g(x,u, Vu) = f, in unbounded domains O, where A is a Lerray-Lions operator from the Weighted Sobolev space W0 1,p(O,w) to its dual, while g(x; s,E ) is a nonlinear term which has a growth condition with respect to E and no growth with respect to s, but it satisfies a sign condition on s, and f € W-1,p’ (O,w’).