| 分数阶Schrodinger—Kirchhoff方程无穷多高能量解的存在性 |
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| 引用本文： | 徐家发,刘立山,蒋继强.分数阶Schrodinger—Kirchhoff方程无穷多高能量解的存在性[J].数学学报,2020(3):209-220. |
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| 作者姓名： | 徐家发 刘立山 蒋继强 |
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| 作者单位： | 重庆师范大学数学科学学院;曲阜师范大学数学科学学院 |
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| 基金项目： | 国家自然科学基金(11601048,11871302);重庆市自然科学基金面上项目(cstc2019jcyj-msxmX0295);重庆市教委项目(KJQN201800533);重庆师范大学青年拔尖人才资助项目(02030307/0040)。 |
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| 摘 要： | 本文研究如下带有变号势函数的分数阶Schrodinger Kirchhoff方程(a+b∫∫R^N|u(x)-u(y)|^p/|x-y|^N+p^sdxdy)^p-1(-△)p^su+λV(x)|u|^p-2u=f(x,u)-μg(x)|u|^q-2u,x∈R^N.其中s∈(0,1),p∈2,∞),q∈(l,p),a,b>0,λ,μ>0均为正常数,在V,f,g等函数合适的条件下,运用喷泉定理获得该系统无穷多高能量解的存在性.
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| 关 键 词： | 分数阶Schrodinger-Kirchhoff方程 高能量解 喷泉定理 |
Existence of Infinitely Many High Energy Solutions for Fractional Schrodinger-Kirchhoff Equations |
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| Jia Fa XU,Li Shan LIU,Ji Qiang JIANG.Existence of Infinitely Many High Energy Solutions for Fractional Schrodinger-Kirchhoff Equations[J].Acta Mathematica Sinica,2020(3):209-220. |
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| Authors: | Jia Fa XU Li Shan LIU Ji Qiang JIANG |
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| Institution: | (School of Mathematical Sciences,Chongqing Normal University,Chongqing 401331,P.R.China;School of Mathematical Sciences,Qufu Normal University,Qufu 273165,P.R.China) |
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| Abstract: | We study the following fractional Schrodinger-Kirchhoff equations with sign-changing potential function:(a+b∫∫R^N|u(x)-u(y)|^p/|x-y|^N+p^sdxdy)^p-1(-△)p^su+λV(x)|u|^p-2u=f(x,u)-μg(x)|u|^q-2u,x∈R^N.where s∈(0,1),p∈2,∞),q∈(l,p),a,b>0,λ,μ>0are positive constants,and by some appropriate assumptions on V,f,p,we use the fountain theorem to obtain the existence of infinitely many high energy solutions for the above system. |
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| Keywords: | fractional Schrodinger-Kirchhoff equations high energy solutions fountain theorem |
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