Article
Ufa Mathematical Journal
Volume 4, Number 2, pp. 74-79
Periodic solutions telegraph equation with
Galikhanov I.F., Pavlenko V.N.
Download PDF
Article on MathNetAbstact
We consider telegraph equations with discontinuous by phase variable inner energy and homogeneous Dirichlet boundary condition. Question of existence of general periodic solutions in the resonant case, when operator created by linear part of the equation with homogeneous Dirichlet boundary condition and condition of periodicity has non zero kernel, and nonlinearity appearing in the equation is limited. Topological method obtained an existence theorem for general periodic solution. The proof is based on the principle of Leray-Schauder for convex compact mappings. The main difference from similar results of other authors - an assumption breaks by phase variable inner energy in telegraph equation.