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Existence Of Solutions For A Wave Equation With Non-Monotone Nonlinearity And A Small Parameter, Jose F. Caicedo, Alfonso Castro, Rodrigo Duque
Existence Of Solutions For A Wave Equation With Non-Monotone Nonlinearity And A Small Parameter, Jose F. Caicedo, Alfonso Castro, Rodrigo Duque
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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.