带Sobolev临界指数的p-Kirchhoff拟线性方程组无穷多解的存在性  

Infinitely Many Solutions for Nonlocal P-Kirchhoff Systems with Critical Exponent

作　　者：张文丽[1] ZHANG Wen-li(Department of Mathematics,Changzhi University,Changzhi 046011,China)

机构地区：[1]长治学院数学系,山西长治046011

出　　处：《数学的实践与认识》2021年第13期257-268,共12页Mathematics in Practice and Theory

基　　金：山西省高等学校教学改革创新重点项目(J2020320)。

摘　　要：研究了有界域上带Sobolev临界指数项和非局部项的p-Kirchhoff拟线性方程组问题,首先研究了问题对应的次临界扰动问题解的存在性,然后通过对次临界扰动问题的解序列紧性的分析,借助次临界扰动问题的无穷多解和最大最小值定理证明了方程组存在无穷多高能量的解.In this paper,we consider a nonlocal p-Kirchhoff systems with critical exponent on a smooth bounded domainΩ(?)R~N.Firstly,the existence of the subcritical perturbation problem solutions corresponding to the problem is studied,and then,through analysising tightness of the solution sequences for the subcritical perturbation problem,the infinite solutions of the subcritical perturbation problem and maximin theorem are used to prove that the critical problem has an infinite number of high energy solutions.

关 键 词：无穷多高能量解 p-Kirchhoff拟线性方程组 指标理论 最大最小值定理 

分 类 号：O241.6[理学—计算数学]