Rocky Mountain Journal of Mathematics

Infinitely many solutions of systems of Kirchhoff-type equations with general potentials

Guofeng Che and Haibo Chen

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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.

Article information

Source
Rocky Mountain J. Math., Volume 48, Number 7 (2018), 2187-2209.

Dates
First available in Project Euclid: 14 December 2018

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1544756807

Digital Object Identifier
doi:10.1216/RMJ-2018-48-7-2187

Mathematical Reviews number (MathSciNet)
MR3892130

Zentralblatt MATH identifier
06999260

Subjects
Primary: 35B38: Critical points 35J50: Variational methods for elliptic systems

Keywords
Kirchhoff-type equations nontrivial solutions sublinear genus theory

Citation

Che, Guofeng; Chen, Haibo. Infinitely many solutions of systems of Kirchhoff-type equations with general potentials. Rocky Mountain J. Math. 48 (2018), no. 7, 2187--2209. doi:10.1216/RMJ-2018-48-7-2187. https://projecteuclid.org/euclid.rmjm/1544756807


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