一类拟线性p-KirchhofF型方程多解的存在性  

Multiple Solutions for a Class of Quasilinear p-Kirchhoff Equation

作　　者：王倩 陈林 WANG Qian;CHEN Lin(College of Mathematics and Statistic,Yili Normal University,Yining 835000,China)

机构地区：[1]伊犁师范大学数学与统计分院,新疆伊宁835000

出　　处：《数学的实践与认识》2020年第18期223-232,共10页Mathematics in Practice and Theory

基　　金：新疆高校科研计划重点资助项目(XJEDU2016I043)。

摘　　要：研究一类无界区域上的p-Kirchhoff型椭圆问题■弱解的存在性.其中Ω是R^N(N>1)中一边界光滑的有界区域的外部区域.1<p<N,λ∈R^1\{0}是参数,权函数V(x),f(x),g(x)满足一定的条件.利用Nehari流形和纤维环映射方法证明了此问题至少存在两个弱解.In this paper,we study the existence of nontrivial solutions for a class of quasilinear p-Kirchhoff equation■whereΩis the complement of a smooth bounded domain in R^N(N≥3).1<p<N andλ∈R^1\{0}is a parameter.The weight functions V(x),f(x)and g(x)satisfy some conditions.We will prove that the problem has at least two solutions by using the Nehari manifold and fibering maps associated with the Euler function for this problem.

关 键 词：椭圆方程 NEHARI流形 p-Kirchhoff型方程 

分 类 号：O175.25[理学—数学]