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Energy scattering for radial focusing inhomogeneous bi-harmonic Schrödinger equations

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Abstract

This note studies the asymptotic behavior of global solutions to the fourth-order Schrödinger equation

$$\begin{aligned} i\dot{u}+\Delta ^2 u+F(x,u)=0 . \end{aligned}$$

Indeed, for both cases, local and non-local source term, the scattering is obtained in the focusing mass super-critical and energy sub-critical regimes, with radial setting. This work uses a new approach due to Dodson and Murphy (Proc Am Math Soc 145(11):4859–4867, 2017).

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Authors and Affiliations

  1. Department of Mathematics, College of Sciences and Arts of Uglat Asugour, Qassim University, Buraydah, Kingdom of Saudi Arabia

    Tarek Saanouni

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  1. Tarek Saanouni
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Correspondence to Tarek Saanouni.

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Communicated by A. Malchiodi.

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Saanouni, T. Energy scattering for radial focusing inhomogeneous bi-harmonic Schrödinger equations. Calc. Var. 60, 113 (2021). https://doi.org/10.1007/s00526-021-01973-z

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