Nonexistence of global solutions to Klein-Gordon equations with variable coefficients power-type nonlinearities

Abstract: In this article, we investigate the Cauchy problem for Klein-Gordon equations with combined power-type nonlinearities. Coefficients in the nonlinearities depend on the space variable. They are sign preserving functions except one of the coefficients, which may change its sign. We study completely the structure of the Nehari manifold. By using the potential well method, we give necessary and sufficient conditions for nonexistence of global solution for subcritical initial energy by means of the sign of the Nehari functional. When the energy is positive, we propose new sufficient conditions for finite time blow up of the weak solutions. One of these conditions is independent of the sign of the scalar product of the initial data. We also prove uniqueness of the weak solutions under slightly more restrictive assumptions for the powers of the nonlinearities.

Object Details

• Location: Deutsche Nationalbibliothek Frankfurt am Main
• Extent: Online-Ressource
• Language: Englisch

References and Relationships

• Bibliographic citation: Nonexistence of global solutions to Klein-Gordon equations with variable coefficients power-type nonlinearities ; volume:21 ; number:1 ; year:2023 ; extent:22 ; Open mathematics ; 21, Heft 1 (2023) (gesamt 22)

Contributors, Places and Time

• Creator: Kolkovska, Natalia ; Dimova, Milena ; Kutev, Nikolai

Further information

• DOI: 10.1515/math-2022-0584
• URN: urn:nbn:de:101:1-2023060214104978152959
• Rights: Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
• Last update: 14.08.2025, 10:55 AM CEST