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The existence of a ground-state solution for a class of Kirchhoff-type equations in ℝN

Part of: Partial differential equations Miscellaneous topics - Partial differential equations

Published online by Cambridge University Press:  03 March 2016

Jiu Liu ,
Jia-Feng Liao  and
Chun-Lei Tang
Jiu Liu
Affiliation:
School of Mathematics and Statistics, Southwest University, Chongqing 400715, People’s Republic of China
Jia-Feng Liao
Affiliation:
School of Mathematics and Statistics, Southwest University, Chongqing 400715, People’s Republic of China and School of Mathematics and Computational Science, Zunyi Normal College, Zunyi, Guizhou 563002, People’s Republic of China
Chun-Lei Tang
Affiliation:
School of Mathematics and Statistics, Southwest University, Chongqing 400715, People’s Republic of China (tangcl@swu.edu.cn)
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Abstract

In this paper, we study the following Kirchhoff-type equation: where a, b are positive constants and N = 1, 2, 3. Under appropriate assumptions on V, K and g, we obtain a ground-state solution by using the approach developed by Szulkin and Weth in 2010.

Keywords

Kirchhoff-type equationNehari manifoldlack of compactnessconcentration-compactness principle

MSC classification

Primary: 35R09: Integro-partial differential equations 35A15: Variational methods 35B09: Positive solutions
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 146 , Issue 2 , April 2016 , pp. 371 - 391
Copyright
Copyright © Royal Society of Edinburgh 2016 

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