Periodic solutions of the nonlinear telegraph equations with bounded nonlinearities

In this article, using the Leray–Schauder degree theory, we discuss existence, nonexistence and multiplicity for the periodic solutions of the nonlinear telegraph equationutt−uxx+cut+Φ(u)=f(t,x)+s,utt−uxx+cut+Φ(u)=f(t,x)+s, where c>0c>0, Φ∈C(R)Φ∈C(R), f∈C(T2)f∈C(T2) and s is a parameter.