Positive solutions for some asymptotically linear and superlinear weighted problems

In this paper, we study the following nonlinear elliptic problem -div(a(x) ?u) = f (x,u), x ? u H10(?) (P) where is a regular bounded domain in RN, N 2, a(x) positive function and reaction source strongly asymptotically linear sense lim t?+? f(x,t)/t q(x) uniformly ?. We use variant version of Mountain Pass Theorem to prove that has solution for large class (x,t) q(x). Here, existence proved without neither Ambrosetti-Rabionowitz condition nor one its refinements. As second result, same techniques solutions when superlinear subcritical on t at infinity.