Periodic solutions for some double-delayed differential equations. (English) Zbl 1367.34092
Summary: We prove the existence of positive \(\omega \)-periodic solutions for the double-delayed differential equation
\[
x^{\prime}(t)-a(t)g(x(t))x(t)=-\lambda (b(t)f(x(t-\tau (t))+c(t)h(x(t-\nu (t))),
\]
where \(\lambda \) is a positive parameter, \(a,b,c,\tau ,\nu \in C(\mathbb {R}, \mathbb {R})\) are \(\omega \)-periodic functions with \(a,b\geq 0,a\), \(b\not \equiv 0\), \(f,g,h\in C([0,\infty ),\mathbb {R})\) with \(g>0\) on \((0,\infty )\), \(h\) is bounded, \(f\) is either superlinear or sublinear at \(\infty\) and could change sign.
MSC:
| 34K13 | Periodic solutions to functional-differential equations |
| 47N20 | Applications of operator theory to differential and integral equations |
| 37C60 | Nonautonomous smooth dynamical systems |
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