A semilinear wave equation with smooth dataand  no  resonance having no continuous solution

José F. Caicedo; Alfonso Castro

doi:10.3934/dcds.2009.24.653

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2009, Volume 24, Issue 3: 653-658. Doi: 10.3934/dcds.2009.24.653

This issue Previous Article Preface Next Article Stability and uniqueness of traveling waves for system of nonlocal evolution equations with bistable nonlinearity

A semilinear wave equation with smooth data and no resonance having no continuous solution

José F. Caicedo^1, and
Alfonso Castro^2,

1.
Departamento de Matemáticas, Universidad Nacional de Colombia, Bogotá
2.
Department of Mathematics, Harvey Mudd College, Claremont, CA 91711

Received: January 2008

Revised: March 2008

Published: September 2009

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Abstract

We prove that a boundary value problem for a semilinear wave equation with smooth nonlinearity, smooth forcing, and no resonance cannot have continuous solutions. Our proof shows that this is due to the non-monotonicity of the nonlinearity.

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Mathematics Subject Classification: 34B15, 35J65.

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