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arXiv · 2403.19284

Existence of solutions for a class of Kirchhoff-type equations with indefinite potential

Linlian Xiao·Jiaqian Yuan·Jian Zhou·Yunshun Wu
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Abstract

In this paper, we consider the existence of solutions of the following Kirchhoff-type problem \[ \left\{ \begin{array} [c]{ll} -\left(a+b\int_{\mathbb{R}^3}|\nabla u|^2dx\right)\Delta u+ V(x)u=f(x,u),~{\rm{in}}~ \mathbb{R}^{3},\\ u\in H^1(\mathbb{R}^3), \end{array} \right. \] where $a,b$ are postive constants, and the potential $V(x)$ is continuous and indefinite in sign. Under some suitable assumptions on $V(x)$ and $f$, we obtain the existence of solutions by the Symmetric Mountain Pass Theorem.

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Linlian Xiao, Jiaqian Yuan, Jian Zhou, Yunshun Wu. 2024-03-28. Existence of solutions for a class of Kirchhoff-type equations with indefinite potential. https://arxiv.org/abs/2403.19284

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