Existence and nonexistence of nontrivial solutions for Choquard type equations
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Date
2016-01-04
Authors
Wang, Tao
Journal Title
Journal ISSN
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.
Rights
Attribution 4.0 International