On The Existence Of Solutions For A Class Of P-Laplacian Equation With Coercive Supercritical Term

This paper deals with a class of p-Laplacian equation with Direchlet boundary value problem, where the nonlinear term is coercive and supercritical, (?),λis a real parameter,Ωis a bounded smooth domain in Rn(n≥3),f:Ω×R→R. We obtained a global minimizer by using Direct Variational method and established a Mountain-Pass solution by using Mountain-Pass Lemma.The problem of this paper comes from Infinite dimensional dynamic system, where we needed studying the complexity of the global attractor of the evolution equations, a good supercritical term|u|r-2u is different from classically super-critical term -|u|r-2u.