一类具有Hardy-Sobolev临界指数的Kirchhoff方程的多解性  

Multiple Solutions for a Class of Kirchhoff-Type Equations with Hardy-Sobolev Critical Exponent

作　　者：苑紫冰 欧增奇[1] YUAN Zi-bing;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：《西南师范大学学报（自然科学版）》2021年第8期32-36,共5页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11801465,11971393).

摘　　要：考虑一类Kirchhoff方程{-a+b∫_(Ω)|▽u|^(2)dxΔu=u^(3)/|x|+λu^(q) x∈Ωu=0x∈∂Ω其中ΩR^(3)是具有光滑边界的有界区域,且0∈Ω,a,b,λ>0,1<q<3.当b>1/A^(2)_(1)时(其中A_(1)>0是最佳Hardy-Sobolev常数),应用山路定理得到了这类带有Hardy-Sobolev临界指数的Kirchhoff方程两个正解的存在性.Consider a class of Kirchhoff equations{-a+b∫_(Ω)|▽u|^(2)dxΔu=u^(3)/|x|+λu^(q) x∈Ωu=0x∈∂ΩWhereΩR^(3)is a bounded domain with smooth boundary and 0∈Ω,a,b,λ>0,1<q<3.When b>1/A^(2)_(1)(where A1 is the best Hardy-Sobolev constant),the existence of two positive solutions of the equation can be obtained by using the Mountain Pass Theorem and some lemmas.

关 键 词：KIRCHHOFF方程 HARDY-SOBOLEV临界指数 山路定理 正解 

分 类 号：O176.3[理学—数学]