Existence of solutions for a class of nonlinear Choquard equations with critical growth. Issue 3 (17th February 2021) - Ao, Yong
ABSTRACT: In this paper, we consider the nonlinear Choquard equation of the form − Δ u + u = ( I α ∗ | u | p ) | u | p − 2 u + | u | q − 2 u in R N, where I α is a Riesz potential, α ∈ ( 0, N ), N ⩾ 4, p = N + α N − 2, 2 < q < 2 ∗ . We show the existence of a nontrivial solution of the equation. Moreover, we consider the corresponding minimizing problem and obtain a nonnegative minimizer.