EXISTENCE OF MULTIPLE SOLUTIONS FOR A FRACTIONAL p-LAPLACIAN SYSTEM WITH CONCAVE-CONVEX TERM

数学物理学报(英文版) ›› 2018, Vol. 38 ›› Issue (6): 1821-1832.

EXISTENCE OF MULTIPLE SOLUTIONS FOR A FRACTIONAL p-LAPLACIAN SYSTEM WITH CONCAVE-CONVEX TERM

谢君辉, 黄孝忠, 陈以平

Department of Mathematics, Hubei University for Nationalities, Enshi 445000, China

收稿日期:2017-09-02 修回日期:2018-04-23 出版日期:2018-12-25 发布日期:2018-12-28
作者简介:Junhui XIE,E-mail:smilexiejunhui@hotmail.com;Xiaozhong HUANG,E-mail:huangzheren@126.com;Yiping CHEN,E-mail:chenyiping66@gmail.com
基金资助:
This work was supported by the National Natural Science Foundation of China (11761030), Hubei Provincial Natural Science Foundation of China (2017CFB352), Doctoral Science Research Foundation of Hubei University for Nationalities (MY2013B019) and Youth Research Foundation of Hubei Institute for Nationalities (MY2017Q023).

EXISTENCE OF MULTIPLE SOLUTIONS FOR A FRACTIONAL p-LAPLACIAN SYSTEM WITH CONCAVE-CONVEX TERM

Junhui XIE, Xiaozhong HUANG, Yiping CHEN

Department of Mathematics, Hubei University for Nationalities, Enshi 445000, China

Received:2017-09-02 Revised:2018-04-23 Online:2018-12-25 Published:2018-12-28
Supported by:
This work was supported by the National Natural Science Foundation of China (11761030), Hubei Provincial Natural Science Foundation of China (2017CFB352), Doctoral Science Research Foundation of Hubei University for Nationalities (MY2013B019) and Youth Research Foundation of Hubei Institute for Nationalities (MY2017Q023).

摘要/Abstract

摘要： In this article, we study the existence of multiple solutions for the following system driven by a nonlocal integro-differential operator with zero Dirichlet boundary conditions

where Ω is a smooth bounded domain in Rⁿ, n > ps with s ∈ (0, 1) fixed, a(x), b(x), c(x) ≥ 0 and a(x), b(x), c(x) ∈ L^∞(Ω), 1< q < p and α, β > 1 satisfy p < α +β < p^*, p^*=np/n-ps. By Nehari manifold and fibering maps with proper conditions, we obtain the multiplicity of solutions to problem (0.1).

关键词: fractional p-Laplacian system, Nehari manifold, multiple solutions

Abstract: In this article, we study the existence of multiple solutions for the following system driven by a nonlocal integro-differential operator with zero Dirichlet boundary conditions

where Ω is a smooth bounded domain in Rⁿ, n > ps with s ∈ (0, 1) fixed, a(x), b(x), c(x) ≥ 0 and a(x), b(x), c(x) ∈ L^∞(Ω), 1< q < p and α, β > 1 satisfy p < α +β < p^*, p^*=np/n-ps. By Nehari manifold and fibering maps with proper conditions, we obtain the multiplicity of solutions to problem (0.1).

Key words: fractional p-Laplacian system, Nehari manifold, multiple solutions

谢君辉, 黄孝忠, 陈以平. EXISTENCE OF MULTIPLE SOLUTIONS FOR A FRACTIONAL p-LAPLACIAN SYSTEM WITH CONCAVE-CONVEX TERM[J]. 数学物理学报(英文版), 2018, 38(6): 1821-1832.

Junhui XIE, Xiaozhong HUANG, Yiping CHEN. EXISTENCE OF MULTIPLE SOLUTIONS FOR A FRACTIONAL p-LAPLACIAN SYSTEM WITH CONCAVE-CONVEX TERM[J]. Acta mathematica scientia,Series B, 2018, 38(6): 1821-1832.

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EXISTENCE OF MULTIPLE SOLUTIONS FOR A FRACTIONAL p-LAPLACIAN SYSTEM WITH CONCAVE-CONVEX TERM

EXISTENCE OF MULTIPLE SOLUTIONS FOR A FRACTIONAL p-LAPLACIAN SYSTEM WITH CONCAVE-CONVEX TERM

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