Existence and nonexistence of nontrivial solutions for Choquard type equations

Date

2016-01-04

Authors

Wang, Tao

Journal Title

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Volume Title

Publisher

Texas State University, Department of Mathematics

Abstract

In this article, we consider the nonlocal problem -Δu + u = q(x) (∫ℝN q(y)|u(y)|p/|x-y|N-α dy) |u|p-2u, x ∈ ℝN, where N ≥ 3, α ∈ (0, N), N+α/N < p < N+α/N-2 and q(x) is a given potential. Under suitable assumptions on q(x), we prove the existence and nonexistence of nontrivial solutions.

Description

Keywords

Choquard equation, Nonlocal nonlinearities, Variational methods

Citation

Wang, T. (2016). Existence and nonexistence of nontrivial solutions for Choquard type equations. <i>Electronic Journal of Differential Equations, 2016</i>(03), pp. 1-17.

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Attribution 4.0 International

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