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2017 Positive ground state solutions for some non-autonomous Kirchhoff type problems
Qilin Xie, Shiwang Ma
Rocky Mountain J. Math. 47(1): 329-350 (2017). DOI: 10.1216/RMJ-2017-47-1-329

Abstract

In this paper, we study the existence of positive ground state solutions for non-autonomous Kirchhoff type problems: $$ -\Big (1+b\int _{\mathbb R^3} |\nabla u|^2\Big ) \Delta u+u=a(x)|u|^{p-1}u \quad \mbox {in } \mathbb {R}^3, $$ where $b>0$, $3\lt p\lt 5$ and $a:\mathbb R^3\rightarrow \mathbb R$ is such that $$ \lim _{|x|\rightarrow \infty } a(x)=a_\infty >0, $$ but no symmetry property on $a(x)$ is required.

Citation

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Qilin Xie. Shiwang Ma. "Positive ground state solutions for some non-autonomous Kirchhoff type problems." Rocky Mountain J. Math. 47 (1) 329 - 350, 2017. https://doi.org/10.1216/RMJ-2017-47-1-329

Information

Published: 2017
First available in Project Euclid: 3 March 2017

zbMATH: 1378.35128
MathSciNet: MR3619766
Digital Object Identifier: 10.1216/RMJ-2017-47-1-329

Subjects:
Primary: 35J60
Secondary: 35J20, 47J30

Rights: Copyright © 2017 Rocky Mountain Mathematics Consortium

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Vol.47 • No. 1 • 2017
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