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On the inhomogeneous biharmonic nonlinear Schrödinger equation: Local, global and stability results
Nonlinear Analysis: Real World Applications ( IF 2 ) Pub Date : 2020-06-20 , DOI: 10.1016/j.nonrwa.2020.103174
Carlos M. Guzmán , Ademir Pastor

We consider the inhomogeneous biharmonic nonlinear Schrödinger equation (IBNLS) iut+Δ2u+λ|x|b|u|αu=0, where λ=±1 and α, b>0. We show local and global well-posedness in Hs(RN) in the Hs-subcritical case, with s=0,2. Moreover, we prove a stability result in H2(RN), in the mass-supercritical and energy-subcritical case. The fundamental tools to prove these results are the standard Strichartz estimates related to the linear problem.



中文翻译:

关于非齐次双调和非线性Schrödinger方程:局部,整体和稳定性结果

我们考虑非均匀双调和非线性Schrödinger方程(IBNLS) 一世üŤ+Δ2ü+λ|X|-b|ü|αü=0 哪里 λ=±1个αb>0。我们展示了本地和全球的良好定位Hs[Rñ 在里面 Hs-次临界情况 s=02。此外,我们证明了稳定性结果H2[Rñ,在质量超临界和能量亚临界的情况下。证明这些结果的基本工具是与线性问题有关的标准Strichartz估计。

更新日期:2020-06-23
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