Multiplicity of standing wave solutions of nonlinear Schrodinger equations with electromagnetic fields

作者：Tang Zhongwei^*

来源：Zeitschrift fur Angewandte Mathematik und Physik, 2008, 59(5): 810-833.

DOI：10.1007/s00033-007-7032-8

• Nonlinear Schrodinger equation
• multiplicity
• potential well
• magnetic fields
• variational methods

In this paper, we are concerned with the multiplicity of standing wave solutions of nonlinear Schrodinger equations with electromagnetic fields
-(del + iA(x))(2)u(x) + (lambda a(x) + 1)u(x) = vertical bar u(x)vertical bar(p-2)u(x), x is an element of R-N (S-lambda)
for sufficient large,, where i is the imaginary unit, 2 < p < 2N/N-2 for N >= 3 and 2 < p < + infinity for N = 1, 2. a( x) is a real continuous function on RN, A( x) = (A(1)( x), A(2)( x),..., A(N)( x)) is such that A(j)( x) is a real local Holder continuous function on R-N for j = 1, 2,..., N. We assume that a( x) is nonnegative and has a potential well Omega := int a(-1)(0) consisting of k components Omega(1),..., Omega(k). We show that for any non-empty subset J subset of {1, 2,..., k}, (S-lambda) has a standing wave solution which is trapped in a neighborhood of boolean OR(j is an element of J)Omega(j) for lambda large.

• 出版日期2008-9
• 单位北京师范大学