Multiple solutions for nonhomogeneous Choquard equations

Abstract

<p>In this article, we consider the multiple solutions for the nonhomogeneous Choquard equations</p> <pre>-∆u + u = (1/|x|^α ∗ |u|^p)|u|^p-2 u + h(x), x ∈ ℝ^N,</pre> <p>and</p> <pre>-∆u = (1/|x|^α ∗ |u|^2*α)|u|^2*α-2u + h(x), x ∈ ℝ^N,</pre> <p>where N ≥ 3, 0 < α < N, 2 - α/N < p < 2*_α = 2N-α/N-2. Under suitable assumptions on h, we obtain at least two solutions on the subcritical case 2 - α/N < p < 2*_α and on the critical case p = 2*_α.</p>