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Research articles

ScienceAsia 45(2019): 279-284 |doi: 10.2306/scienceasia1513-1874.2019.45.279


Multiple solutions for k-coupled Schrödinger system with variable coefficients


Xin Wang, Lijie Yin, Xiaorui Yue*

 
ABSTRACT:     Consider the k-coupled Schrödinger system with variable coefficients as below which arises in nonlinear optics and other physical problems:


where Ω is a bounded smooth domain in R N , N ≤ 3, k≥ 2; λj > −λ1 (Ω) for j = 1, . . . , k and λ1 (Ω) is the first eigenvalue of −∆ with Dirichlet boundary condition; µj (x) and βi j(x) = βji(x) are positive bounded functions for i, j ≠, . . . , k, i 6= j. We obtain multiple solutions with some components sign-changing while the others positive, and one positive solution for the above problem.

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a College of Information Science and Technology, Hainan University, Haikou, Hainan 570228, China

* Corresponding author, E-mail: yxr@hainu.edu.cn

Received 8 Oct 2018, Accepted 28 May 2019