Multiple sign-changing and semi-nodal solutions for coupled Schrodinger equations

作者：Chen, Zhijie; Lin, Chang-Shou; Zou, Wenming^*

来源：Journal of Differential Equations, 2013, 255(11): 4289-4311.

DOI：10.1016/j.jde.2013.08.009

• BOUND-STATES
• POSITIVE SOLUTIONS
• R-N
• SYSTEM
• COMPETITION
• WAVES

We study the following coupled Schrodinger equations which have appeared as several models from mathematical physics:
{-Delta u(1) + lambda(1)u(1) = mu(1)u(1)(3) + beta u(1)u(2)(2), x is an element of Omega,
-Delta u(2) + lambda(2)u(2) = mu(2)u(2)(3) + beta u(1)u(2)(2), x is an element of Omega,
u(1) = u(2) = 0 on partial derivative Omega.
Here Omega subset of R-N (N = 2,3) is a smooth bounded domain, lambda(l), lambda(2), mu(1), mu(2) are all positive constants. We show that, for each k is an element of N there exists beta(k) > 0 such that this system has at least k sign-changing solutions (i.e., both two components change sign) and k semi-nodal solutions (i.e., one component changes sign and the other one is positive) for each fixed beta is an element of (0, beta(k)).

• 单位
  清华大学