分数阶Schrödinger-Kirchhoff 方程无穷多高能量解的存在性

徐家发, 刘立山, 蒋继强

数学学报 ›› 2020, Vol. 63 ›› Issue (3) : 209-220.

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数学学报 ›› 2020, Vol. 63 ›› Issue (3) : 209-220. DOI: 10.12386/A2020sxxb0017
论文

分数阶Schrödinger-Kirchhoff 方程无穷多高能量解的存在性

    徐家发1, 刘立山2, 蒋继强2
作者信息 +

Existence of Infinitely Many High Energy Solutions for Fractional Schrödinger-Kirchhoff Equations

    Jia Fa XU1, Li Shan LIU2, Ji Qiang JIANG2
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摘要

本文研究如下带有变号势函数的分数阶Schrödinger-Kirchhoff方程

其中s∈(0,1),p∈[2,∞),q∈(1,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.

Abstract

We study the following fractional Schrödinger-Kirchhoff equations with sign-changing potential function:

where s ∈ (0,1), p ∈[2, ∞), q ∈ (1, p), a, b > 0, λ, μ > 0 are positive constants, and by some appropriate assumptions on V, f, g, we use the fountain theorem to obtain the existence of infinitely many high energy solutions for the above system.

关键词

分数阶Schrö / dinger-Kirchhoff方程 / 高能量解 / 喷泉定理

Key words

fractional Schrödinger-Kirchhoff equations / high energy solutions / fountain theorem

引用本文

导出引用
徐家发, 刘立山, 蒋继强. 分数阶Schrödinger-Kirchhoff 方程无穷多高能量解的存在性. 数学学报, 2020, 63(3): 209-220 https://doi.org/10.12386/A2020sxxb0017
Jia Fa XU, Li Shan LIU, Ji Qiang JIANG. Existence of Infinitely Many High Energy Solutions for Fractional Schrödinger-Kirchhoff Equations. Acta Mathematica Sinica, Chinese Series, 2020, 63(3): 209-220 https://doi.org/10.12386/A2020sxxb0017

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基金

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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