Unstable Ground State and Blow Up Result of Nonlocal Klein–Gordon Equations

In this paper we study the behaviour of solutions for a nonlocal hyperbolic equation. We use the Pohozaev manifold combined with a new technique to explicit two invariant regions in the space of initial data. On the first one the solution blows up (in finite or infinite time) and in the second one t...

Full description

Saved in:
Bibliographic Details
Published in:Journal of dynamics and differential equations 2023-09, Vol.35 (3), p.1917-1945
Main Authors: Carrião, Paulo Cesar, Lehrer, Raquel, Vicente, André
Format: Article
Language:English
Subjects:
Applications of Mathematics
Ground state
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper we study the behaviour of solutions for a nonlocal hyperbolic equation. We use the Pohozaev manifold combined with a new technique to explicit two invariant regions in the space of initial data. On the first one the solution blows up (in finite or infinite time) and in the second one the solution exists globally. Additionally, we prove that the ground state solution of the elliptic problem associated to the original problem is unstable. The main goal of this paper is to present a new technique which allows us to consider nonlocal problems and to extend the classical result proved by Shatah (Trans Am Math Soc 290(2):701–710, 1985).
ISSN:1040-7294
1572-9222
DOI:10.1007/s10884-023-10281-3