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

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