Article - postprint
For double-periodic and Dirichlet-periodic boundary conditions, we prove the existence of solutions to a forced semilinear wave equation with asymptotically linear nonlinearity, no resonance, and non-monotone nonlinearity when the forcing term is not flat on characteristics. The solutions are in L∞ when the forcing term is in L∞ and continous when the forcing term is continuous. This is in contrast with the results in , where the non-enxistence of continuous solutions is established even when forcing term is of class C∞ but is flat on a characteristic.
© 2010 American Institute of Mathematical Sciences
Castro, Alfonso and Benjamin Preskill. “Existence of solutions for a semilinear wave equation with non-monotone nonlinearity”, Continuous and Discrete Dynamical Systems, Series A, Vol. 28, No. 2, (2010), pp. 649-658.