一类高维Laplace方程的拟周期解(英文)

QUASI-PERIODIC SOLUTIONS OF A CLASS OF HIGHER DIMENSIONAL LAPLACE EQUATIONS

本文利用KAM理论,证明了一类带有常位势m(m>2)以及Fourier乘子M_ξ的高维Laplace方程△u+(m+M_ξ)u+u^3=0,在周期边值条件下拟周期解的存在性。

In this paper, we prove the existence of plenty of quasi-periodic soltuions for the higher dimensional Laplace equations with constant potential m 〉 2 and Fourier multiplier Mξ △u ＋ （m ＋ Mξ）u ＋ u^3 = 0, subject to periodic boundary conditions via KAM theory