Existence of nontrivial solutions for a perturbation of Choquard equation with Hardy-Littlewood-Sobolev upper critical exponent

Abstract

<p>In this article, we consider the problem</p> <pre>-∆u = (∫_ℝ^N |u|^2*_μ/|x - y|^μ dy) |u|^2*_μ - 2 u + ƒ(x, u) in ℝ^N,</pre> <p>where N ≥ 3, μ ∈ (0, N) and 2*_μ = 2N - μ/N - 2. Under suitable assumptions on ƒ(x, u), we establish the existence and non-existence of nontrivial solutions via the variational method.</p>