一类p-拉普拉斯方程解的存在性和集中紧性

Existence and Concentration of Solutions to a Class of p-Laplace Equations

摘要: 文章研究了如下形式的 p-Laplace 方程: -Δ_pu+λV(x)|u|^P-2 u=f(x,u),x∈ℝ^N, u∈W^1,p(ℝ^N), 其中参数λ>0, V∈C(R^N, R⁺)且V ^-1(0)内部非空。在一些较弱的假设条件下，本文讨论了该方程非平凡解的存在性以及当λ→∞时该方程解的集中紧性，所得结果推广了相关文献的研究成果。

Abstract: This article concerns the p-Laplace equations: -Δ_pu+λV(x)|u|^P-2 u=f(x,u),x∈ℝ^N, u∈W^1,p(ℝ^N), where λ>0 is a parameter, V∈C(R^N, R⁺)and V ^-1(0) has nonempty interior. Under some mild assumptions, the existence of nontrivial solutions of the equation is obtained by using the variational method. Moreover, the concentration of solutions is also explored.