Existence of $L^p$-solutions for a semilinear wave equation with non-monotone nonlinearity
Existence of $L^p$-solutions for a semilinear wave equation with non-monotone nonlinearity
For Dirichlet-periodic and double periodic boundary conditions, we prove the existence of solutions to aforced semilinear wave equation with large forcing terms not flat oncharacteristics. The nonlinearity is assumed to be non-monotone, asymptotically linear, and not resonanant.We prove that the solutions are in $L^{p}$, $(p\geq 2)$, when the forcing term …