一类Choquard型方程解的存在性

数学物理学报 ›› 2018, Vol. 38 ›› Issue (1): 54-60.

一类Choquard型方程解的存在性

孙小妹

华中农业大学理学院武汉 430070

收稿日期:2017-01-13 修回日期:2017-04-15 出版日期:2018-02-26 发布日期:2018-02-26
作者简介:孙小妹,xmsunn@mail.hzau.edu.cn
基金资助:
国家自然科学基金（11601173）

The Existence of Solutions for Choquard Type Equation

Sun Xiaomei

College of Science, Huazhong Agricultural University, Wuhan 430070

Received:2017-01-13 Revised:2017-04-15 Online:2018-02-26 Published:2018-02-26
Supported by:
Supported by the NSFC (11601173)

摘要/Abstract

摘要： 该文研究如下形式的Choquard型方程
-Δ_pu+V（x）|u|^p-2u=（|x|^-（N-α）*F（u））f（u），
其中，-Δ_pu=div（|▽u|^p-2▽u），x=（y，z）∈R^K×R^N-K.假定混合位势V（y，z）关于y具有周期性，关于z具有强制性，并且非线性项f满足一定的条件，利用变分理论，该文证明了上述Choquard型方程具有山路水平解.

关键词: Choquard型方程, 混合位势, 非平凡解

Abstract: In this paper, we consider the following Choquard type equation
-Δ_pu+V(x)|u|^p-2u=(|x|^-(N-α) * F(u))f(u),
where -Δ_pu=div(|▽ u|^p-2▽ u) and x=(y,z)∈ R^K×R^N-K. Assume that the potential V(y,z) and the nonlinearity f satisfy suitable conditions, we prove the existence of solutions in the level of mountain pass for the above Choquard equation.

Key words: Choquard type equation, Mixted potential, Nontrivial solution

中图分类号:

O175.25

孙小妹. 一类Choquard型方程解的存在性[J]. 数学物理学报, 2018, 38(1): 54-60.

Sun Xiaomei. The Existence of Solutions for Choquard Type Equation[J]. Acta mathematica scientia,Series A, 2018, 38(1): 54-60.

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