Existence of solutions of elliptic boundary value problems with mixed type nonlinearities

We study the existence of a nontrivial solution of the following elliptic boundary value problem with mixed type nonlinearities: {-Delta u = f(x,u) in Omega, {u = 0 on partial derivative Omega, where f(x,u) = -K-u + W-u. We consider the problem in a different case: lim(vertical bar u vertical bar ->infinity)f(x, u)/u = infinity, lim(vertical bar u vertical bar -> 0) f(x,u)/u is some constant. Assuming that K satisfies the "pinching" condition, and W satisfies a more general superquadratic growth condition than the well-known Ambrosetti-Rabinowitz condition usually used in literature, we obtain a nontrivial solution via the Mountain Pass Lemma.