含参数拟线性非齐次椭圆型方程的多重解  

Multiple Solutions for Quasilinear Nonhomogeneous Elliptic Equations with a Parameter

作　　者：宋洪雪[1,2] 魏云峰 Hongxue Song;Yunfeng Wei(School of Science, Nanjing University of Posts and Telecommunications, Nanjing 210023;College of Science, Hohai University, Nanjing 210098;School of Statistics and Mathematics, Nanjing Audit University, Nanjing 211815)

机构地区：[1]南京邮电大学理学院,南京210023 [2]河海大学理学院,南京210098 [3]南京审计大学统计与数学学院,南京211815

出　　处：《数学物理学报（A辑）》2019年第2期286-296,共11页Acta Mathematica Scientia

基　　金：国家自然科学基金(61503198);中国博士后科学基金面上项目(2017M611664);南京邮电大学校级科研基金(NY217092;NY218076)~~

摘　　要：该文研究如下形式的拟线性非齐次椭圆型方程-△_pu-△_p(|u|^(2α))|u|^(2α-2)u+V(x)|u|^(p-2)u=h(u)+g(x), x∈R^N,其中1 <p≤N (N≥3),1/2 <α≤1,V∈C(R^N,R), h∈C(R,R),而且扰动项g∈L^p'(R^N),这里p'=p/(p-1).利用变量代换结合极小极大方法可以证明该问题存在多重解.In this paper, we study the following quasilinear nonhomogeneous elliptic equations of the form -△pu-△p(|u|^2α)|u|^2α-2u+V(x)|u|^p-2u=h(u)+g(x), x∈R^N, where 1<p≤N(N≥3), 1/2<α≤1, V∈C(RN,R), h∈C(R,R) and g∈L^p′(R^N), where p′=p/p-1, is a disturbance term. Using a variable replacement and minimax method, we show the existence and multiplicity of solutions to this problem.

关 键 词：拟线性椭圆型方程 EKELAND变分原理 P-S序列 

分 类 号：O175.25[理学—数学]