带有凹凸非线性项的Kirchhoff型方程解的多重性  

Multiplicity of Solutions for Kirchhoff Equation with Concave and Convex Nonlinearities

作　　者：王雅琪 欧增奇[1] WANG Ya-qi;OU Zeng-qi(School of Mathematics and Statistics,Southwest University,Chongqing 400715,China)

机构地区：[1]西南大学数学与统计学院,重庆400715

出　　处：《西南大学学报（自然科学版）》2018年第10期89-94,共6页Journal of Southwest University(Natural Science Edition)

基　　金：国家自然科学基金项目(11471267)

摘　　要：利用集中紧性原理和对偶喷泉定理,研究了一类带有凹凸非线性项的Kirchhoff方程{-(a+b∫Ω|▽u|~2dx )Δu=|u|~4u+μ|u|^(q-2)u x∈Ω u=0 x∈?Ω获得了该方程有无穷多个解.其中Ω为R^3中边界光滑的有界开集,且a,b>0,1<q <2,μ>0.In this paper,we study a class of Kirchhoff equation {-（a＋b∫Ω｜▽u｜^2dx ）Δu=｜u｜~4u＋μ｜u｜^q-2u x∈Ω u=0 x∈δΩ with concave and convex nonlinearities,where Ω R^3 is a smooth bounded domain with a,b〉0,1〈q〈2,μ〉0.By means of the concentration compactness principle and a dual fountain theorem,we obtain the multiplicity of solutions about this equation.

关 键 词：KIRCHHOFF方程 凹凸非线性项 集中紧性原理 对偶喷泉定理 

分 类 号：O176.3[理学—数学]