Singular Choquard elliptic problems involving two nonlocal nonlinearities via the nonlinear Rayleigh quotient

2024/12/19 by Edcarlos D. Silva, Silva, Edcarlos D., da Rocha, Marlos R. +2
Mathematics · #Differential Equations and Boundary Problems #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2412.14940

Abstract

In the present work we shall consider the existence and multiplicity of solutions for nonlocal elliptic singular problems where the nonlinearity is driven by two convolutions terms. More specifically, we shall consider the following Choquard type problem: \-Δu+V(x)u=λ(I_α1*a|u|^q)a(x)|u|^q-2u+μ(I_α2*|u|^p)|u|^p-2u u∈ H¹(ℝ^N). where α₂<α₁; α₁,α₂∈(0,N) and 0 0 such that our main problem has at least two solutions using the Nehari method. Here we also use the Rayleigh quotient for the following scenarios λ∈ (0, λ^*) and λ= λ^*. Moreover, we consider some decay estimates ensuring a non-existence result for the Choquard type problems in the whole space.

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