Multi-Peak Solutions for Coupled Nonlinear Schrodinger Systems in Low Dimensions

作者：Zhen, Maoding; Zhang, Binlin; Radulescu, Vicentiu D.^*

来源：Applied Mathematics and Optimization, 2023, 88(1): 4.

DOI：10.1007/s00245-023-09974-4

• Nonlinear Schrodinger system
• Lyapunov-Schmidt reduction
• Singularity
• Perturbation

In this paper, we construct the solutions to the following nonlinear Schrodinger system @@@ [GRAPHICS] @@@ . @@@ where 3 < p < +infinity, N is an element of {1, 2}, epsilon > 0 is a small parameter, the potentials P, Q satisfy 0 < P-0 <= P(x) <= P-1 and Q(x) satisfies 0 < Q(0) <= Q(x) <= Q(1). We construct the solution for attractive and repulsive cases. When x(0) is a local maximum point of the potentials P and Q and P(x(0)) = Q(x0), we construct k spikes concentrating near the local maximum point x(0). When x(0) is a local maximum point of P and (x) over bar (0) is a local maximum point of Q, we construct k spikes of u concentrating at the local maximum point x(0) and m spikes of v concentrating at the local maximum point (x) over bar (00) when x(0) not equal (x) over bar (0)0. This paper extends the main results established by Peng and Wang (Arch Ration Mech Anal 208:305-339, 2013) and Peng and Pi (Discrete Contin Dyn Syst 36:2205-2227, 2016), where the authors considered the case N = 3, p = 3.