Bifurcation at infinity for a semilinear wave equation with non-monotone nonlinearity

José Caicedo; Alfonso Castro; Arturo Sanjuán

doi:10.3934/dcds.2017078

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2017, Volume 37, Issue 4: 1857-1865. Doi: 10.3934/dcds.2017078

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Bifurcation at infinity for a semilinear wave equation with non-monotone nonlinearity

1.
Departamento de Matemáticas, Universidad Nacional de Colombia, Bogotá, Colombia
2.
Department of Mathematics, Harvey Mudd College, Claremont, CA 91711, USA
3.
Proyecto Curricular de Matemáticas, Universidad Distrital Francisco José de Caldas, Bogotá, Colombia

Author Bio: E-mail address: jfcaicedoc@unal.edu.co; E-mail address: castro@g.hmc.edu; E-mail address: aasanjuanc@udistrital.edu.co

Received: April 30, 2016

Revised: October 31, 2016

Published: May 2017

This work was partially supported by a grant from the Simons Foundations (# 245966 to Alfonso Castro).

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Abstract

We prove bifurcation at infinity for a semilinear wave equation depending on a parameter $λ$ and subject to Dirichlet-periodic boundary conditions. We assume the nonlinear term to be asymptotically linear and not necessarily monotone. We prove the existence of L^∞ solutions tending to $+∞$ when the bifurcation parameter approaches eigenvalues of finite multiplicity of the wave operator. Further details are presented in cases of simple eigenvalues and odd multiplicity eigenvalues.

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Mathematics Subject Classification: Primary:35L75;Secondary:34B16.

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References

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