Multiple entire solutions for Schrödinger-Hardy systems involving two fractional operators
Minimax theory and its applications, Tome 4 (2019) no. 1
The paper is devoted to the study of the following fractional Schrödinger-Hardy system in Rn ∆s mu ax um−2u μ um−2u xms Hux,u,v , ∆s pv bx vp−2v σ vp−2v xps Hvx,u,v , where μ and σ are real parameters, dimension n > ps, with s , , < m p<m∗ s mn/n ms , a and b are positive potentials, while Hu and Hv are derivatives of a suitable continuous function H. The main feature of the paper is the combination of two possibly different fractional operators and different Hardy terms with a nonlinearity H which does not necessarily satisfy the Ambrosetti-Rabinowitz condition. By using the symmetric mountain pass theorem, we provide the existence of an unbounded sequence of nonnegative entire solutions. For this, we complete the picture of the existence result stated in Theorem 1.1 by the author, P.Pucci and S.Saldi in [“Existence of entire solutions for Schrödinger-Hardy systems involving the fractional p-Laplacian”, Nonlinear Anal. 158 (2017) 109–131].
Mots-clés :
Schrödinger-Hardy systems, existence of entire solutions, fractional p-Laplacian op erator
@article{MTA_2019_4_1_a6,
author = {Alessio Fiscella},
title = {Multiple entire solutions for {Schr\"odinger-Hardy} systems involving two fractional operators},
journal = {Minimax theory and its applications},
year = {2019},
volume = {4},
number = {1},
zbl = {1421.35108},
url = {http://geodesic.mathdoc.fr/item/MTA_2019_4_1_a6/}
}
Alessio Fiscella. Multiple entire solutions for Schrödinger-Hardy systems involving two fractional operators. Minimax theory and its applications, Tome 4 (2019) no. 1. http://geodesic.mathdoc.fr/item/MTA_2019_4_1_a6/