Differential and Integral Equations

Logarithmic NLS equation on star graphs: Existence and stability of standing waves

Alex H. Ardila

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Abstract

In this paper, we consider the logarithmic Schrödinger equation on a star graph. By using a compactness method, we construct a unique global solution of the associated Cauchy problem in a suitable functional framework. Then we show the existence of several families of standing waves. We also prove the existence of ground states as minimizers of the action on the Nehari manifold. Finally, we show that the ground states are orbitally stable via a variational approach.

Article information

Source
Differential Integral Equations, Volume 30, Number 9/10 (2017), 735-762.

Dates
First available in Project Euclid: 27 May 2017

Permanent link to this document
https://projecteuclid.org/euclid.die/1495850425

Mathematical Reviews number (MathSciNet)
MR3656485

Zentralblatt MATH identifier
06770140

Subjects
Primary: 76B25: Solitary waves [See also 35C11] 35Q51: Soliton-like equations [See also 37K40] 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10] 35J60: Nonlinear elliptic equations 37K40: Soliton theory, asymptotic behavior of solutions 34B37: Boundary value problems with impulses

Citation

Ardila, Alex H. Logarithmic NLS equation on star graphs: Existence and stability of standing waves. Differential Integral Equations 30 (2017), no. 9/10, 735--762. https://projecteuclid.org/euclid.die/1495850425


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