Article - postprint
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.
© 2009 American Institute of Mathematical Sciences
Caicedo, Jose F. and Alfonso Castro. “A semilinear wave equation with smooth data and no resonance having no continuous solution,” Continuous and Discrete Dynamical Systems, Series A, Vol. 24, No. 3 (2009), pp. 653-658.