On the existence of multiple normalized solutions for a class of fractional Choquard equations with mixed nonlinearities

2024/11/03 by Chen, Yongpeng, Yang, Zhipeng, Zhang, Jianjun · 3 citations
#35A15 #35B40 #35J20 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2411.01476

Abstract

We investigate the existence of normalized solutions for the following nonlinear fractional Choquard equation: (-Δ)^s u+V(εx)u=λu+(I_α*|u|^q)|u|^q-2 u+(I_α*|u|^p)|u|^p-2 u, x ∈ ℝ^N, subject to the constraint ∫_ℝ^N|u|² dx=agt;0, where N>2 s, s ∈(0,1), α∈(0, N), (N+α)/(N)0 is a parameter, and λ∈ ℝ serves as an unknown parameter acting as a Lagrange multiplier. By employing the Lusternik-Schnirelmann category theory, we estimate the number of normalized solutions to this problem by virtue of the category of the set of minimum points of the potential function V.

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• Normalized solutions for a class of fractional Choquard equations with mixed nonlinearities
• Multiplicity of normalized solutions to the upper critical fractional Choquard equation with L²-supercritical perturbation
• On the existence of normalized solutions to a class of fractional Choquard equation with potentials

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