## Annals of Functional Analysis

### A note on fourth-order nonlinear Schrödinger equation

Tarek Saanouni

#### Abstract

We consider in four space dimensions, the initial value problem for a fourth-order semi-linear Schröodinger equation with exponential type nonlinearity. In the defocusing sign, we obtain unconditional global well-posedness in the energy space. In the focusing case, global well-posedness via existence of ground state holds for small radial data.

#### Article information

Source
Ann. Funct. Anal., Volume 6, Number 1 (2015), 249-266.

Dates
First available in Project Euclid: 19 December 2014

https://projecteuclid.org/euclid.afa/1419001464

Digital Object Identifier
doi:10.15352/afa/06-1-19

Mathematical Reviews number (MathSciNet)
MR3297801

Zentralblatt MATH identifier
1316.35268

#### Citation

Saanouni, Tarek. A note on fourth-order nonlinear Schrödinger equation. Ann. Funct. Anal. 6 (2015), no. 1, 249--266. doi:10.15352/afa/06-1-19. https://projecteuclid.org/euclid.afa/1419001464

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