Normalized solutions for a system of coupled cubic Schrodinger equations on R-3

作者：Bartsch, Thomas; Jeanjean, Louis; Soave, Nicola^*

来源：Journal de Mathematiques Pures et Appliquees, 2016, 106(4): 583-614.

DOI：10.1016/j.matpur.2016.03.004

• Nonlinear Schrodinger systems
• Normalized solutions
• Orbital stability
• Minimax principle

We consider the system of coupled elliptic equations @@@ {(-Delta u - lambda(1)u = mu(1)u(3) + beta uv(2) in R-3,R- @@@ -Delta v - lambda(2)v = mu(2)v(3) + beta u(2)v @@@ and study the existence of positive solutions satisfying the additional condition @@@ (R3)integral u(2) = a(1)(2) and (R3)integral v(2) = a(2)(2). @@@ Assuming that a(1), a(2), mu(1), mu(2) are positive fixed quantities, we prove existence results for different ranges of the coupling parameter beta > 0. The extension to systems with an arbitrary number of components is discussed, as well as the orbital stability of the corresponding standing waves for the related Schrodinger systems.

• 出版日期2016-10