%0 Journal Article
%T 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
%A 刘文静
%J Pure Mathematics
%P 333-341
%@ 2160-7605
%D 2025
%I Hans Publishing
%R 10.12677/PM.2025.155182
%X 文章研究了如下形式的 p-Laplace 方程:
-Δpu+λV(x)|μ|P-2
u=f(x,μ),x∈？N,
μ∈W1,p(？N),
其中参数λ>0, V∈C(RN, 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。
This article concerns the p-Laplace equations:
-Δpu+λV(x)|μ|P-2
u=f(x,μ),x∈？N,
μ∈W1,p(？N),
where λ>0 is a parameter, V∈C(RN, 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.
%K p-Laplace方程，变分法，非平凡解，集中紧性
p-Laplace Equation
%K Variational Method
%K Nontrivial Solutions
%K Concentration
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=116335