Existence of entire solutions for Schrödinger–Hardy systems involving two fractional operators. (July 2017)

• Record Type: Journal Article
• Authors: Fiscella, Alessio; Pucci, Patrizia; Saldi, Sara
• Is Part Of: Nonlinear analysis. Volume 158(2017)
• Page Start: 109
• Page End: 131
• Publication Date: 2017-07
• Subjects: primary 35J47 35B08 35B09 35R11 -- secondary 35Q55 35B33 47G20; Schrödinger–Hardy systems -- Existence of entire solutions -- Fractional p-Laplacian operator; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2017.04.005
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: This paper deals with the existence of nontrivial nonnegative solutions of Schrödinger–Hardy systems driven by two possibly different fractional ℘ -Laplacian operators, via various variational methods. The main features of the paper are the presence of the Hardy terms and the fact that the nonlinearities do not necessarily satisfy the Ambrosetti–Rabinowitz condition. Moreover, we consider systems including critical nonlinear terms, as treated very recently in literature, and present radial versions of the main theorems. Finally, we briefly show how to extend the previous results when the fractional Laplacian operators are replaced by more general elliptic nonlocal integro–differential operators.