August  2009, 24(3): 653-658. doi: 10.3934/dcds.2009.24.653

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

1. 

Departamento de Matemáticas, Universidad Nacional de Colombia, Bogotá, Colombia

2. 

Department of Mathematics, Harvey Mudd College, Claremont, CA 91711, United States

Received  January 2008 Revised  March 2008 Published  April 2009

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.
Citation: José F. Caicedo, Alfonso Castro. A semilinear wave equation with smooth data and no resonance having no continuous solution. Discrete & Continuous Dynamical Systems - A, 2009, 24 (3) : 653-658. doi: 10.3934/dcds.2009.24.653
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