On the positive vector solutions for nonlinear fractional Laplacian systems with linear coupling
- Resource Type
- Authors
- Shuangjie Peng; Dengfeng Lü
- Source
- Discrete & Continuous Dynamical Systems - A. 37:3327-3352
- Subject
- Class (set theory)
Applied Mathematics
010102 general mathematics
Mathematical analysis
Zero (complex analysis)
Vector Laplacian
01 natural sciences
Linear coupling
010101 applied mathematics
Nonlinear system
Coupling parameter
Discrete Mathematics and Combinatorics
0101 mathematics
Fractional Laplacian
Ground state
Analysis
Mathematics
- Language
- ISSN
- 1553-5231
In this paper, a class of systems of two coupled nonlinear fractional Laplacian equations are investigated. Under very weak assumptions on the nonlinear terms $f$ and $g$, we establish some results about the existence of positive vector solutions and vector ground state solutions for the fractional Laplacian systems by using variational methods. In addition, we also study the asymptotic behavior of these solutions as the coupling parameter $β$ tends to zero.