Existence of positive periodic solutions of nonlinear first-order delayed differential equations

摘要

We consider the existence of positive Ω-periodic solutions for the equation. u'(t)=a(t)g(u(t))u(t)-λb(t)f(u(t-τ(t))), where a,b∈C(R,[0,∞)) are Ω-periodic functions with f0Ωa(t)dt>0, f0Ωb(t)dt>0; f,g∈C([0,∞),[0,∞)) and f(s)>0 for s>0; τ is a continuous Ω-periodic function; λ>0 is a parameter. The proofs of our main results are based upon fixed point index theory.