Non-linear bi-harmonic Choquard equations

Tarek Saanouni

doi:10.3934/cpaa.2020221

Article Contents

2020, Volume 19, Issue 11: 5033-5057. Doi: 10.3934/cpaa.2020221

This issue Previous Article Next Article Quasilinear nonlocal elliptic problems with variable singular exponent

Non-linear bi-harmonic Choquard equations

Tarek Saanouni

Department of Mathematics, College of Science and Arts in Uglat Asugour, Qassim University, Buraydah, Kingdom of Saudi Arabia

Received: December 31, 2019

Revised: March 31, 2020

Early access: July 2020

Published: November 2020

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Abstract

This note studies the fourth-order Choquard equation

$ i\dot u+\Delta^2 u\pm (I_\alpha *|u|^p)|u|^{p-2}u = 0 . $

In the mass super-critical and energy sub-critical regimes, a sharp threshold of global well-psedness and scattering versus finite time blow-up dichotomy is obtained.

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Mathematics Subject Classification: 35Q55.

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