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.
Citation
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
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