MULTIPLICITY AND CONCENTRATION BEHAVIOUR OF POSITIVE SOLUTIONS FOR SCHRÖDINGER-KIRCHHOFF TYPE EQUATIONS INVOLVING THE p-LAPLACIAN IN RN

doi:10.1016/S0252-9602(18)30756-2

数学物理学报(英文版) ›› 2018, Vol. 38 ›› Issue (2): 391-418.doi: 10.1016/S0252-9602(18)30756-2

MULTIPLICITY AND CONCENTRATION BEHAVIOUR OF POSITIVE SOLUTIONS FOR SCHRÖDINGER-KIRCHHOFF TYPE EQUATIONS INVOLVING THE p-LAPLACIAN IN R^N

贾慧芳, 李工宝

Hubei Key Laboratory of Mathematical Sciences and School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China

收稿日期:2017-07-17 修回日期:2017-12-18 出版日期:2018-04-25 发布日期:2018-04-25
通讯作者: Gongbao LI E-mail:ligb@mail.ccnu.edu.cn
作者简介:Huifang JIA,E-mail:hf_jia@mails.ccnu.edu.cn
基金资助:
This work was supported by Natural Science Foundation of China (11371159 and 11771166), Hubei Key Laboratory of Mathematical Sciences and Program for Changjiang Scholars and Innovative Research Team in University #IRT_17R46.

MULTIPLICITY AND CONCENTRATION BEHAVIOUR OF POSITIVE SOLUTIONS FOR SCHRÖDINGER-KIRCHHOFF TYPE EQUATIONS INVOLVING THE p-LAPLACIAN IN R^N

Huifang JIA, Gongbao LI

Hubei Key Laboratory of Mathematical Sciences and School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China

Received:2017-07-17 Revised:2017-12-18 Online:2018-04-25 Published:2018-04-25
Contact: Gongbao LI E-mail:ligb@mail.ccnu.edu.cn
Supported by:
This work was supported by Natural Science Foundation of China (11371159 and 11771166), Hubei Key Laboratory of Mathematical Sciences and Program for Changjiang Scholars and Innovative Research Team in University #IRT_17R46.

摘要/Abstract

摘要：

In this article, we study the multiplicity and concentration behavior of positive solutions for the p-Laplacian equation of Schrödinger-Kirchhoff type
-ε^pM(ε^p-N ∫_R^N|▽u|^p)△_pu + V (x)|u|^p-2u=f(u)
in R^N, where △_p is the p-Laplacian operator, 1< p < N, M:R⁺→ R⁺ and V:R^N → R⁺ are continuous functions, ε is a positive parameter, and f is a continuous function with subcritical growth. We assume that V satisfies the local condition introduced by M. del Pino and P. Felmer. By the variational methods, penalization techniques, and LyusternikSchnirelmann theory, we prove the existence, multiplicity, and concentration of solutions for the above equation.

关键词: Schrödinger-Kirchhoff type equation, variational methods, multiple positive solutions, concentrating solution, penalization method

Abstract:

Key words: Schrödinger-Kirchhoff type equation, variational methods, multiple positive solutions, concentrating solution, penalization method

贾慧芳, 李工宝. MULTIPLICITY AND CONCENTRATION BEHAVIOUR OF POSITIVE SOLUTIONS FOR SCHRÖDINGER-KIRCHHOFF TYPE EQUATIONS INVOLVING THE p-LAPLACIAN IN R^N[J]. 数学物理学报(英文版), 2018, 38(2): 391-418.

Huifang JIA, Gongbao LI. MULTIPLICITY AND CONCENTRATION BEHAVIOUR OF POSITIVE SOLUTIONS FOR SCHRÖDINGER-KIRCHHOFF TYPE EQUATIONS INVOLVING THE p-LAPLACIAN IN R^N[J]. Acta mathematica scientia,Series B, 2018, 38(2): 391-418.

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MULTIPLICITY AND CONCENTRATION BEHAVIOUR OF POSITIVE SOLUTIONS FOR SCHRÖDINGER-KIRCHHOFF TYPE EQUATIONS INVOLVING THE p-LAPLACIAN IN R^N

MULTIPLICITY AND CONCENTRATION BEHAVIOUR OF POSITIVE SOLUTIONS FOR SCHRÖDINGER-KIRCHHOFF TYPE EQUATIONS INVOLVING THE p-LAPLACIAN IN R^N

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