Electron. J. Diff. Equ., Vol. 2016 (2016), No. 149, pp. 1-15.

Existence and nonexistence of solutions of asymptotically linear Klein-Gordon equation

Paulo C. Carriao, Raquel Lehrer, Andre Vicente

Abstract:
In this article we study a nonlinear Klein-Gordon equation when the nonlinear term asymptotically linear at infinity. We used the Pohozaev manifold to separate a subspace of R^N on a global existence region and on a blow up region.

Submitted December 15, 2015. Published June 17, 2016.
Math Subject Classifications: 35L15, 35L70, 35B40, 35B44, 35A01, 35A15.
Key Words: Klein-Gordon equation; blow up of solution; asymptotically linear; Pohozaev manifold.

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Paulo C. Carrião
Universidade Federal de Minas Gerais - ICEX - Matemática
CEP: 31270-901, Belo Horizonte, MG, Brazil
email: pauloceca@gmail.com
Raquel Lehrer
Universidade Estadual do Oeste do Paraná - CCET
Rua Universitária, 2069, Jd. Universitário
CEP: 85819-110, Cascavel, PR, Brazil
email: rlehrer@gmail.com
André Vicente
Universidade Estadual do Oeste do Paraná - CCET
Rua Universitária, 2069, Jd. Universitário
CEP: 85819-110, Cascavel, PR, Brazil
email: andre.vicente@unioeste.br

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