In this paper, we study the following nonlinear elliptic problem −div(a(x)u) = f (x, u), x ∈ Ω u ∈ H 1 0 (Ω) (P) where Ω is a regular bounded domain in R N , N ≥ 2, a(x) a bounded positive function and the nonlinear reaction source is strongly asymptotically linear in the following sense lim t→+∞ f (x, t) t = q(x) uniformly in x ∈ Ω. We use a variant version of Mountain Pass Theorem to prove that the problem (P) has a positive solution for a large class of f (x, t) and q(x). Here, the existence of solution is proved without use neither the Ambrosetti-Rabionowitz condition nor one of its refinements. As a second result, we use the same techniques to prove the existence of solutions when f (x, t) is superlinear and subcritical on t at infinity