一类具有Robin边值条件的 p-Laplace方程解的存在性

Existence of Solutions for a Class of p-Laplace Equations Involving Robin Boundary Value Conditions

摘要: 研究了一类具有Robin边值条件的p-Laplace方程解的存在性.利用Sobolev紧嵌入定理以及给定的假设条件证明了该类方程的能量泛函具有山路型结构并且满足(PS)条件,从而根据山路引理得到了该类方程在Sobolev空间W^1,p(Ω)中非平凡弱解的存在性.

Abstract: A probe is made into the existence of a class of p-Laplace equations with Robin boundary value condition. By applying the Sobolev compact embedding theorem and assumptions given, it is proven that the energy functional of this type of equations is of a Mountain Pass type structure and satisfies the(PS)condition. Consequently, the existence of the nontrivial weak solutions of the p-Laplace equations in the Sobolev spaceW^1,p(Ω)is obtained by the use of the Mountain Pass Lemma.