New existence results for nonlinear delayed differential systems at resonance

This paper deals with the first-order delayed differential systems u'+a(t)u=h(t)v+f(t,u(t-τ (t))), v'+b(t)v=g(t,u(t-τ (t))), where a , b , τ , h are continuous ω -periodic functions with ∫_0^ωa(t) dt=0 and ∫_0^ωb(t) dt>0 ; f∈ C(ℝ× [0,∞ ),ℝ) and g∈ C( ℝ× [0,∞ ),[0,∞ )) are ω -periodic with respect to t . By means of the fixed point theorem in cones, several new existence theorems on positive periodic solutions are established. Our main results enrich and complement those available in the literature.