Ruowen Qiu, Renqing You, Fukun Zhao
Abstract:
In this article, we consider the nonlocal schr\"odinger equation
$$
-\mathcal{L}_K u+V(x)u=f(x,u),\quad x\in\mathbb{R}^N,
$$
where \(-\mathcal{L}_K\) is an integro-differential operator and
\(V\) is coercive at infinity, and \(f(x,u)\) is asymptotically linear
for \(u\) at infinity. Combining minimax method and invariant set of
descending flow, we prove that the problem possesses infinitely many
sign-changing solutions.
Submitted September 9, 2024. Published January 15, 2025.
Math Subject Classifications: 35R11, 35A15, 35B28.
Key Words: Sign-changing solution; integro-differential operator; invariant set; variational method.
DOI: 10.58997/ejde.2025.07
Show me the PDF file (413 KB), TEX file for this article.
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Ruowen Qiu Department of Mathematics Yunnan Normal University Kunming, 650221, China email: 1239814486@qq.com |
|---|---|
| Renqing You Department of Mathematics Yunnan Normal University Kunming, 650221, China email: 1768332868@qq.com | |
| Fukun Zhao Department of Mathematics Yunnan Normal University Kunming, 650221, China email: fukunzhao@163.com |
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