Multiple Entire Solutions for Schrödinger-Hardy Systems Involving Two Fractional Operators
Keywords:
Schrödinger-Hardy systems, existence of entire solutions, fractional p-Laplacian op erator.Abstract
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].
Downloads
Downloads
Published
Issue
Section
License
You are free to:
- Share — copy and redistribute the material in any medium or format for any purpose, even commercially.
- Adapt — remix, transform, and build upon the material for any purpose, even commercially.
- The licensor cannot revoke these freedoms as long as you follow the license terms.
Under the following terms:
- Attribution — You must give appropriate credit , provide a link to the license, and indicate if changes were made . You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.
Notices:
You do not have to comply with the license for elements of the material in the public domain or where your use is permitted by an applicable exception or limitation .
No warranties are given. The license may not give you all of the permissions necessary for your intended use. For example, other rights such as publicity, privacy, or moral rights may limit how you use the material.
