Electronic Journal of Differential Equations, Vol. 2023 (2023), No. 75, pp. 1-20.

Title: Concentration of nodal solutions for semiclassical quadratic Choquard equations
       
Authors: Lu Yang (Yunnan Univ., Kunming, China)
         Xiangqing Liu (Yunnan Normal Univ., Kunming, China)
         Jianwen Zhou (Yunnan Univ., Kunming, China)
         
Abstract:
In this article concerns the semiclassical Choquard equation
$-\varepsilon^2 \Delta u +V(x)u = \varepsilon^{-2}( \frac{1}{|\cdot|}* u^2)u$ 
for $x \in \mathbb{R}^3$ and small $\varepsilon$.
We establish the existence of a sequence of localized nodal solutions
concentrating near a given local minimum point of the potential function $V$,
by means of the perturbation method and the method of invariant sets of
descending flow.

Submitted May 18, 2023. Published October 30, 2023.
Math Subject Classifications: 35B05, 35B45.
Key Words: Choquard equation; sign-changing solution; perturbation method; Fredholm operator; nodal solution.