Positive doubly periodic solutions of nonlinear telegraph equations Original Research Article

This paper deals with the existence of nontrivial doubly periodic solutions for the nonlinear telegraph equation View the MathML source where c>0 is a constant, View the MathML source, View the MathML source, and a,b,f are 2π-periodic in t and x. We show the existence of positive doubly periodic weak solutions when 0⩽a(t,x)⩽c2/4 and f is either superlinear or sublinear on u by using the Krasnoselskiiʹs fixed point theorem in cones.