Existence of solutions for a class of nonlinear Choquard equations with critical growth. Issue 3 (17th February 2021)

• Record Type: Journal Article
• Authors: Ao, Yong
• Is Part Of: Applicable analysis. Volume 100:Issue 3(2021)
• Page Start: 465
• Page End: 481
• Publication Date: 2021-02-17
• Subjects: Nonlinear Choquard equations -- Nehari manifold -- variational methods -- Schwarz rearrangement; 35Q55 -- 35R09 -- 35J91; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2019.1608961
• Languages: English
• ISSNs: 0003-6811

Abstract

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.