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arXiv · 1812.00223

Time Asymptotic expansions of solution for fourth-order Schr\"odinger equation with zero resonance or eigenvalue

Hongliang Feng·Zhao Wu·Xiaohua Yao
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Abstract

In this paper, we first deduce the asymptotic expansions of resolvent of $H=(-\Delta)^2+V$ with the presence of resonance or eigenvalue at the degenerate zero threshold for $d\geq5$. In particular, we identify these resonance spaces for full kinds of zero resonances. As a consequence, we then establish the {\it time asymptotic expansions} and {\it Kato-Jensen estimates} for the solution of fourth-order Schr\"odinger equation under the presence of zero resonance or eigenvalue.

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Hongliang Feng, Zhao Wu, Xiaohua Yao. 2018-12-01. Time Asymptotic expansions of solution for fourth-order Schr\"odinger equation with zero resonance or eigenvalue. https://arxiv.org/abs/1812.00223

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