Normalized solutions for a class of fractional Choquard equations with mixed nonlinearities

2025/12/18 by Chen, Shaoxiong, Yang, Zhipeng, Zhang, Xi
#35A15 #35B40 #35J20 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2512.16438

Abstract

In this paper we study the following fractional Choquard equation with mixed nonlinearities: \ (-Δ)^s u = λu + α( I_μ* |u|^q ) |u|^q-2 u + ( I_μ* |u|^p ) |u|^p-2 u, x ∈ ℝ^N,
∫_ℝ^N |u|² dx = c² · gt; 0. . Here N > 2s, s ∈ (0,1), μ∈ (0, N), and the exponents satisfy (2N - μ)/(N) lt; q lt; p lt; (2N - μ)/(N - 2s), while α> 0 is a sufficiently small parameter, λ∈ ℝ is the Lagrange multiplier associated with the mass constraint, and I_μ denotes the Riesz potential. We establish existence and multiplicity results for normalized solutions and, in addition, prove the existence of ground state normalized solutions for α in a suitable range.

Citations

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