Time Asymptotic expansions of solution for fourth-order Schrödinger equation with zero resonance or eigenvalue

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 $d\ge 5$. 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 Schrödinger equation under the presence of zero resonance or eigenvalue.

arXiv comment35 pages. This is an updated version, where more backgrounds and comments are added

References in corpus (4)

• Dispersive Estimates for higher dimensional Schrödinger Operators with threshold eigenvalues I: The odd dimensional case
• Time decay for solutions of Schrödinger equations with rough and time dependent potentials
• Dispersive Estimates for higher dimensional Schrödinger Operators with threshold eigenvalues II: The even dimensional case
• On the Fourth order Schrödinger equation in three dimensions: dispersive estimates and zero energy resonances

Cited by in corpus (5)

• On the Fourth order Schrödinger equation in three dimensions: dispersive estimates and zero energy resonances
• On the $L^p$ boundedness of the Wave Operators for fourth order Schrödinger operators
• Dispersive estimates for inhomogeneous fourth-order Schrödinger operator in 3D with zero energy obstructions
• Decay estimates for higher order elliptic operators
• Decay estimates for fourth-order Schrödinger operators in dimension two