Electronic Journal of Differential Equations, Vol. 2025 (2025), No. 07, pp. 1-19.

Title: Infinitely many sign-changing solutions for an asymptotically linear and nonlocal schrodinger equation

Authors: Ruowen Qiu (Yunnan Normal Univ., Kunming, China)
         Renqing You (Yunnan Normal Univ., Kunming, China)
         Fukun Zhao (Yunnan Normal Univ., Kunming, China)
  
Abstract:
In this article, we consider the  nonlocal schrodinger 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.