带有变号非线性项Kirchhoff方程基态解的存在性  

Existence of Ground State Solutions for Kirchhoff Equation with Sign-changing Nonlinearities

作　　者：耿茜 李宇华[1] 

机构地区：[1]山西大学数学科学学院,山西太原030006

出　　处：《河南科技大学学报（自然科学版）》2019年第3期90-94,111,共6页Journal of Henan University of Science And Technology:Natural Science

基　　金：国家自然科学基金项目(11301313;11571209;11671239);山西省自然科学基金项目(2015021007)

摘　　要：研究了一类带有变号非线性项Kirchhoff方程基态解的存在性。由于非线性项是变号的,相应的Nehari流形不再是一阶连续可微的。因此,利用Nehari流形和单位球面拓扑同胚的性质,将此类方程转化在工作空间的单位球面上来考虑。然后,在此单位球面上利用Ekelend变分原理找到有界极小化序列。最后,利用反证法证明了基态解的存在性。The existence of ground state solutions for a kind of Kirchhoff equation with sign-changing nonlinearities was studied. Because of the nonlinearities were sign-changing, the corresponding Nehari manifold was not first order continuous and differentiable any more. Therefore,by using of the property that Nehari manifold was topological homeomorphism with unit sphere,this kind of equation was transformed on the unit sphere. Then,the bounded minimizing sequence was found by using of Ekelend variational principle on the unit sphere. Finally,the existence of the ground state solution was proved with reduction to absurdity.

关 键 词：变号非线性项 NEHARI流形 KIRCHHOFF方程 极小化序列 基态解 

分 类 号：O177.91[理学—数学]