Article - postprint
We provide sufficient conditions for the existence of solutions to a semilinear wave equation with non-monotone nonlinearity involving a small parameter. Our results are based on the analysis of a an operator that characterizes the projection onto the kernel of the wave operator subject to periodic-Dirichlet boundary conditions. Such a kernel is infinite dimensional which makes standard compactness arguments inapplicable.
© 2011 Springer Verlag
Caicedo, Jose F., Alfonso Castro and Rodrigo Duque. "Existence of Solutions for a Wave Equation with Non-monotone Nonlinearity and a Small Parameter", Milan Journal of Mathematics, Volume 79, Number 1, (2011), pp. 207-220.