Multi-bump bound states of nonlinear Schrodinger equations with electromagnetic fields and critical frequency

作者：Tang Zhongwei^*

来源：Journal of Differential Equations, 2008, 245(10): 2723-2748.

DOI：10.1016/j.jde.2008.07.035

• Nonlinear Schrodinger equation
• Multi-bump standing waves
• Potential well
• Magnetic fields
• Variational methods

In this paper, we are concerned with the existence and asymptotic behavior of standing wave solution psi(x,t)= e-(i lambda Et) of nonlinear Schrodinger equations with electromagnetic fields i partial derivative psi/partial derivative t = -(del + iA(x))(2)psi + lambda W(x)psi - f(|psi|(2))psi, (t,x) is an element of R x R-N,R- with E being a critical frequency in the sense that inf(x is an element of RN) W(x)=E. We show that if the zero set of W - E has several isolated connected components Omega(1),...., Omega(k) such that the interior of Omega(i) is not empty and partial derivative Omega(i) is smooth, then for lambda > 0 large there exists, for any non-empty subset J subset of (1,2,...,k), a standing wave solution which is trapped in a neighborhood of boolean OR(jeJ) Omega(j).

• 出版日期2008-11-15
• 单位北京师范大学