Existence Of Nontrivial Solution For A P-Laplace Equation

In this paper, we are concerned with the existence of the nontrival solution for the following Dirichlet problem for the p-Laplace equation where-△pu=-div(|▽Vu|p-2▽u),p>l,Ω(?)RN(N≥1) is abounded domain with smooth boundary dΩ,f(x, u)～|u|p-2u, as|u|→∞. As we know, this kind of nonlinear term causes some difficulties in applying the mountain pass theorem and in verifying the (PS) condition, be-cause f(x,t) does not satisfy the classical Ambrosetti-Rabinowitz-type condition any more. When λ<λ1, it is known that we can get the existence of solutions for the problem by using mountain pass theorem. But there seems few results for the case of λ≥λ1. In this paper, we use the Linking Theorem to study the existence of solution for λ≥λ1...