带变号非线性项的p-Kirchhoff型问题的多解性（英文）  

Existence of Multiple Solutions for a p-Kirchhoff Problem With Sign-changing Nonlinearity

作　　者：李琴[1] 杨作东[2] 

机构地区：[1]安徽财经大学统计与应用数学学院,蚌埠安徽233030 [2]南京师范大学教师教育学院,南京江苏210097

出　　处：《数学进展》2017年第4期590-598,共9页Advances in Mathematics（China）

基　　金：supported by NSFC(No.11571093,No.11471164);the NSF of Education Bureau of Anhui Province(No.KJ2017A432)

摘　　要：本文主要研究带有零Dirichlet边界条件的p-Kirchhoff型方程(α+λ((∫_Ω(|▽u|~p+V(x)|u|~p)dx)~T)(-△_pu+V(x)|u|^(p-2)u)=f(x,u),x∈Ω解的存在性与多解性,其中Ω是R^N(N≥3)中的有界光滑区域,a,λ>0,τ>0,函数V.f连续且满足一定的条件.利用变分法,得到了该问题无穷多个非平凡解的存在性.In this paper, we study the multiplicity of solutions for the following p-Kirchhoff equation with zero Dirichlet boundary condition, where ~ is a bounded domain with smooth boundary in RN （N ≥ 3）, a, λ〉 0, τ〉 0, and V, f are continuous functions satisfying some conditions. By using the variational method, we get the existence of infinitely many nontrivial solutions for the previous equation.

关 键 词：多解性 p-Kirchhoff型问题 变分法 

分 类 号：O175.2[理学—数学]