分数阶Schrodinger-Kirchhoff型方程无穷多解的存在性  

Infinitely Many Solutions for Schrodinger-Kirchhoff Type Equations Involving the Fractional p-Laplacian

作　　者：熊茶文 陈春芳[1] Xiong Chawen;Chen Chunfang(Department of Mathematics,Nanchang University,Nanchang 330031,China;College of Science,East China Univerisity of Technology,Nanchang 330013,China)

机构地区：[1]南昌大学数学系,江西南昌330031 [2]东华理工大学理学院,江西南昌330013

出　　处：《南开大学学报（自然科学版）》2023年第4期71-80,共10页Acta Scientiarum Naturalium Universitatis Nankaiensis

基　　金：国家自然科学基金(11661053,11771198);江西省社会科学基金(21JY03)。

摘　　要：研究了包含分数阶p-拉普拉斯算子和凹凸非线性项的Schrodinger-Kirchhoff型方程.在对方程中的位势函数作适当假设下,运用山路定理、喷泉定理和Clark定理,证明了上述方程正解的存在性,并进一步证明了方程存在无穷多个非平凡解.The following Schrodinger-Kirchhoff type equations involving the fractional p-Laplacian and a concave-convex term are studied.Under some appropriate assumptions about the potential functions,the existence of positive solutions and infinitely many solutions of this equation are obtained via mountain pass theorem,fountain theorem and Clark theorem.

关 键 词：Schrodinger-Kirchhoff型方程 分数阶p-拉普拉斯算子 喷泉定理 Clark定理 

分 类 号：O175.29[理学—数学]