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2019 On ground state solutions for the nonlinear Kirchhoff type problems with a general critical nonlinearity
Weihong Xie, Haibo Chen
Topol. Methods Nonlinear Anal. 53(2): 519-545 (2019). DOI: 10.12775/TMNA.2019.010

Abstract

In this paper, we are concerned with the following Kirchhoff type problem with critical growth: \begin{equation*} -\bigg(a+b\int_{\mathbb R^3}|\nabla u|^2dx\bigg)\Delta u+V(x)u=f(u)+|u|^4u, \quad u\in H^1(\mathbb R^3), \end{equation*} where $a,b > 0$ are constants. Under certain assumptions on $V$ and $f$, we prove that the above problem has a ground state solution of Nehari-Pohozaev type and a least energy solution via variational methods. Furthermore, we also show that the mountain pass value gives the least energy level for the above problem. Our results improve and extend some recent ones in the literature.

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Weihong Xie. Haibo Chen. "On ground state solutions for the nonlinear Kirchhoff type problems with a general critical nonlinearity." Topol. Methods Nonlinear Anal. 53 (2) 519 - 545, 2019. https://doi.org/10.12775/TMNA.2019.010

Information

Published: 2019
First available in Project Euclid: 10 May 2019

MathSciNet: MR3983984
zbMATH: 07130709
Digital Object Identifier: 10.12775/TMNA.2019.010

Rights: Copyright © 2019 Juliusz P. Schauder Centre for Nonlinear Studies

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Vol.53 • No. 2 • 2019
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