Positive doubly periodic solutions of telegraph equations with delays.

This paper deals with the existence of positive doubly periodic solutions for the nonlinear telegraph equation with delays ...u = f(t,x,u(t-τ1,x),..., u(t-τn,x)), (t,x) ∈ R², where ...u := utt - uxx + cut + a(t, x)u is a linear telegraph operator acting on function u: R²→R, c > 0 is a constant, a ∈ C(R², (0,∞)) is 2π-periodic in t and x,f ∈ C(R² × [0,∞)n, [0,∞)) is 2π-periodic in t and x, and τ1,..., τn ∈ [0,∞) are constants. Some existence results of positive doubly 2π-periodic weak solutions are obtained under that f (t, x,η1,...,ηn) satisfies some superlinear or sublinear growth conditions on η1,...,ηn. The discussion is based on the fixed point index theory in cones. [ABSTRACT FROM AUTHOR]