Multi-peak solutions for nonlinear Choquard equation with a general nonlinearity

Minbo Yang; Jianjun Zhang; Yimin Zhang

doi:10.3934/cpaa.2017025

Article Contents

2017, Volume 16, Issue 2: 493-512. Doi: 10.3934/cpaa.2017025

This issue Previous Article Estimates for eigenvalues of a system of elliptic equations with drift and of bi-drifting laplacian Next Article Liouville theorems for elliptic problems in variable exponent spaces

Multi-peak solutions for nonlinear Choquard equation with a general nonlinearity

1.
Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China
2.
College of Mathematics and Statistics, Chongqing Jiaotong University, Chongqing 400074, China
3.
Department of Mathematics, Wuhan University of Technology, Wuhan 430070, China

Author Bio: E-mail address: mbyang@zjnu.edu.cn; E-mail address: zhangym802@126.com
*Corresponding author
*Corresponding author

Received: March 31, 2016

Revised: October 31, 2016

Published: August 2017

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Abstract

In this paper, we study a class of nonlinear Choquard type equations involving a general nonlinearity. By using the method of penalization argument, we show that there exists a family of solutions having multiple concentration regions which concentrate at the minimum points of the potential V. Moreover, the monotonicity of f(s)=s and the so-called Ambrosetti-Rabinowitz condition are not required.

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Mathematics Subject Classification: Primary: 35B25, 35B33; Secondary: 35J61.

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