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 > 0 is a constant, a11, a22, b1, b2 ∈ C(R2,R+), a12, a21 ∈ C(R2,R−), f, g ∈ C(R2 × R+ × R+,R+), and aij , bi , f , g are 2π-periodic in t and x. We show the existence and multiplicity results when 0 aii (t, x) c2 i4 and f , g are superlinear or sublinear on (u, v) by using the fixed point theorem in cones. © 2007 Elsevier Inc. All rights reserved