Choquard-type equations with Hardy–Littlewood–Sobolev upper-critical growth

Author:

Cassani Daniele1ORCID,Zhang Jianjun2

Affiliation:

1. Dipartimento di Scienza e Alta Tecnologia , Università degli Studi dell’Insubria ; and RISM–Riemann International School of Mathematics, via G.B. Vico 46, 21100 Varese , Italy

2. College of Mathematics and Statistics , Chongqing Jiaotong University , Chongqing 400074 , P. R. China ; and Dipartimento di Scienza e Alta Tecnologia, Università degli Studi dell’Insubria, via G.B. Vico 46, 21100 Varese, Italy

Abstract

Abstract We are concerned with the existence of ground states and qualitative properties of solutions for a class of nonlocal Schrödinger equations. We consider the case in which the nonlinearity exhibits critical growth in the sense of the Hardy–Littlewood–Sobolev inequality, in the range of the so-called upper-critical exponent. Qualitative behavior and concentration phenomena of solutions are also studied. Our approach turns out to be robust, as we do not require the nonlinearity to enjoy monotonicity nor Ambrosetti–Rabinowitz-type conditions, still using variational methods.

Publisher

Walter de Gruyter GmbH

Subject

Analysis

Reference68 articles.

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3. C. O. Alves, J. A. M. do Ó and M. A. S. Souto, Local mountain-pass for a class of elliptic problems in ℝ N {\mathbb{R}^{N}} involving critical growth, Nonlinear Anal. 46 (2001), no. 4, 495–510.

4. C. O. Alves, F. Gao, M. Squassina and M. Yang, Singularly perturbed critical Choquard equations, J. Differential Equations 263 (2017), no. 7, 3943–3988.

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