一类低次幂带调和势的非线性Schrdinger方程的驻波轨道稳定性

Orbital Stability of Standing Waves for a Class of the Lower Power Nonlinear Schrdinger Equations with Harmonic Potentials

研究了一类带调和势的非线性Schrd inger方程iφt=-Δφ+|x|2φ+μ|φ|2φ+λ|φ|4φ,x∈RN,t≥0,其中μ>0,λ>0.采用T.Cazenave和P.L.L ions的方法以及一个紧性引理,得到了其所有驻波的存在性.进一步,证明了其所有驻波是轨道稳定的.

In this paper a class of nonlinear Schrtidinger equations with harmonic potentials are considered iφt=-△φ＋｜x｜^2φ＋μ｜φ｜^2φ＋λ｜φ｜^4φ,x∈R^N,t≥0 whereμ 〉 0,λ 〉 0. By using the method of T. Cazenave and P. L. Lions and a compactness lemma, the existence of all the standing waves is proved. Furthermore, the orbital stability of the standing waves is also obtained.