Nonnegative doubly periodic solutions for nonlinear telegraph system

This paper deals with the nonnegative doubly periodic solutions for nonlinear telegraph system{utt−uxx+c1ut+a11(t,x)u+a12(t,x)v=b1(t,x)f(t,x,u,v),vtt−vxx+c2vt+a21(t,x)u+a22(t,x)v=b2(t,x)g(t,x,u,v), where ci>0ci>0 is a constant, a11,a22,b1,b2∈C(R2,R+)a11,a22,b1,b2∈C(R2,R+), a12,a21∈C(R2,R−)a12,a21∈C(R2,R−), f,g∈C(R2×R+×R+,R+)f,g∈C(R2×R+×R+,R+), and aijaij, bibi, f, g are 2π-periodic in t and x  . We show the existence and multiplicity results when 0⩽aii(t,x)⩽ci24 and f, g   are superlinear or sublinear on (u,v)(u,v) by using the fixed point theorem in cones.