Doubly periodic solutions to a coupled telegraph system (Q412636)

Considered is a system of two nonlinear telegraph equations depending on a parameter and with periodic, in both variables \(t\) and \(x\), boundary conditions. Under some very special conditions for the coefficients and nonlinear terms, existence and multiplicity results for the solution are obtained. For the proof one refers to a fixed point theorem in cones, to be found in [\textit{D. Guo} and \textit{V. Lakshmikantham}, Nonlinear problems in abstract cones. Boston, MA: Academic Press (1988; Zbl 0661.47045)]. The article ends with examples to illustrate the applicability of the results.