LAUSR

We prove the existence of positive $$\omega $$ω-periodic solutions for the double-delayed differential equation $$\begin{aligned} x^{\prime }(t)-a(t)g(x(t))x(t)=-\lambda (b(t)f(x(t-\tau (t))+c(t)h(x(t-\nu (t))), \end{aligned}$$x′(t)-a(t)g(x(t))x(t)=-λ(b(t)f(x(t-τ(t))+c(t)h(x(t-ν(t))),where $$\lambda $$λ is a positive parameter, $$a,b,c,\tau ,\nu \in C(\mathbb {R}, \mathbb {R})$$a,b,c,τ,ν∈C(R,R) are $$\omega $$ω-periodic functions with $$a,b\ge 0,a,b\not \equiv 0,f,g,h\in C([0,\infty ),\mathbb {R})$$a,b≥0,a,b≢0,f,g,h∈C([0,∞),R) with $$g>0$$g>0 on $$(0,\infty ),$$(0,∞),$$\ h$$h is bounded, f is either superlinear or sublinear at $$\infty $$∞ and could change sign.