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2018 Infinitely many solutions of systems of Kirchhoff-type equations with general potentials
Guofeng Che, Haibo Chen
Rocky Mountain J. Math. 48(7): 2187-2209 (2018). DOI: 10.1216/RMJ-2018-48-7-2187

Abstract

This paper is concerned with the following systems of Kirchhoff-type equations: \begin{equation} \begin{cases} -\left (a+b\int _{\mathbb {R}^{N}}|\nabla u|^{2}\mathrm {d}x\right )\Delta u\\ \quad +V(x)u=F_{u}(x, u, v)\quad & x\in \mathbb {R}^{N},\\ -\left (c+d\int _{\mathbb {R}^{N}}|\nabla v|^{2}\mathrm {d}x\right )\Delta v\\ \quad +V(x)v=F_{v}(x, u, v) & x\in \mathbb {R}^{N},\\ u(x)\rightarrow 0,\quad v(x)\rightarrow 0 &\mbox {as } |x|\rightarrow \infty . \end{cases} \end{equation} Under some more relaxed assumptions on $V(x)$ and $F(x, u, v)$, we prove the existence of infinitely many negative-energy solutions for the above system via the genus properties in critical point theory. Some recent results from the literature are greatly improved and extended.

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Guofeng Che. Haibo Chen. "Infinitely many solutions of systems of Kirchhoff-type equations with general potentials." Rocky Mountain J. Math. 48 (7) 2187 - 2209, 2018. https://doi.org/10.1216/RMJ-2018-48-7-2187

Information

Published: 2018
First available in Project Euclid: 14 December 2018

zbMATH: 06999260
MathSciNet: MR3892130
Digital Object Identifier: 10.1216/RMJ-2018-48-7-2187

Subjects:
Primary: 35B38, 35J50

Rights: Copyright © 2018 Rocky Mountain Mathematics Consortium

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Vol.48 • No. 7 • 2018
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