Existence and Multiplicity Results for the Nonlinear Klein-Gordon Equation

In this work, we study the multiplicity of solutions for a stationary nonhomogeneous problem associated to the nonlinear one-dimensional Klein-Gordon Equation. We prove that the existence of positive solutions is equivalent to the solvability of a scalar equation 2F(M) = 1, where F is a real functio...

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Bibliographic Details
Published inApplicable analysis Vol. 82; no. 9; pp. 895 - 903
Main Authors Amster, P., Borgna, J. P., Mariani, M. C., Rial, D. F.
Format Journal Article
LanguageEnglish
Published Taylor & Francis Group 01.09.2003
Subjects
1991 Mathematics Subject Classifications: 34b15
Multiple Solutions
Nonlinear Klein-Gordon Equation
Positive Solutions
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ISSN0003-6811
1563-504X
DOI10.1080/0003681031000154936

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Summary:In this work, we study the multiplicity of solutions for a stationary nonhomogeneous problem associated to the nonlinear one-dimensional Klein-Gordon Equation. We prove that the existence of positive solutions is equivalent to the solvability of a scalar equation 2F(M) = 1, where F is a real function depending on V. Moreover, we prove some existence and multiplicity results for the Dirichlet problem in the superlinear case.
ISSN:0003-6811
1563-504X
DOI:10.1080/0003681031000154936