Normalized solutions for a fractional N/s-Laplacian Choquard equation with exponential critical nonlinearities

2023/10/09 by Chen, Wenjing, Wang, Zexi
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2310.05477

Abstract

In this paper, we are concerned with the following fractional N/s-Laplacian Choquard equation \begincases (-Δ)^s_N/su=λ|u|^(N)/(s)-2u +(I_μ*F(u))f(u), in ℝ^N, ∫_ℝ^N|u|^N/s dx=a^N/s, \endcases where s∈(0,1), 1<(N)/(s)∈ ℕ⁺, a>0 is a prescribed constant, λ∈ ℝ, I_μ(x)=(1)/(|x|^μ) with μ∈(0,N), F is the primitive function of f, and f is a continuous function with exponential critical growth of Trudinger-Moser type. Under some suitable assumptions on f, we prove that the above problem admits a ground state solution for any given a>0, by using the constraint variational method and minimax technique.

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