A semilinear wave equation with smooth data and no resonance having no continuous solution. (English summary) Discrete Contin. Dyn. Syst. 24 (2009), no. 3, 653–658. Summary: “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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