Periodic solutions for some double-delayed differential equations |
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Authors: | D D Hai C Qian |
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Institution: | 1.Department of Mathematics and Statistics,Mississippi State University,Mississippi State,USA |
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Abstract: | We prove the existence of positive \(\omega \)-periodic solutions for the double-delayed differential equation $$\begin{aligned} x^{\prime }(t)-a(t)g(x(t))x(t)=-\lambda (b(t)f(x(t-\tau (t))+c(t)h(x(t-\nu (t))), \end{aligned}$$ where \(\lambda \) is a positive parameter, \(a,b,c,\tau ,\nu \in C(\mathbb {R}, \mathbb {R})\) are \(\omega \)-periodic functions with \(a,b\ge 0,a,b\not \equiv 0,f,g,h\in C(0,\infty ),\mathbb {R})\) with \(g>0\) on \((0,\infty ),\) \(\ h\) is bounded, f is either superlinear or sublinear at \(\infty \) and could change sign. |
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