Almost periodic solutions for a class of higher dimensional Schrodinger equations

作者：Geng Jiansheng^*

来源：Frontiers of Mathematics in China, 2009, 4(3): 463-482.

DOI：10.1007/s11464-009-0029-1

• Schrodinger equation
• almost-periodic solution
• KAM method

In this paper, we show that there are almost periodic solutions corresponding to full dimensional invariant tori for higher dimensional Schrodinger equations with Fourier multiplier iu(t)-Delta u M(xi)u f(|u|(2)) u = 0, subject to periodic boundary conditions, where the nonlinearity f is a real-analytic function near u = 0 with f(0) = 0. The proof is based on an improved infinite dimensional KAM theorem.

• 出版日期2009-9
• 单位南京大学