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We study the existence of a nontrivial solution of the following elliptic boundary value problem with mixed type nonlinearities: {-△u = f (x,u) in ω, {u = 0 on ∂ω where f(x, u) = -Ku + Wu. We consider the problem in a different case: lim\u\→. ∞f(x,u)/u = ∞, lim\u\→o 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. © 2012 Mao et al licensee Springer.

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