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Cheng, Zhibo; Li, Feifan

Positive periodic solutions for a kind of second-order neutral differential equations with variable coefficient and delay. (English) Zbl 1395.34075

Mediterr. J. Math. 15, No. 3, Paper No. 134, 19 p. (2018).
Summary: In this article, we discuss a type of second-order neutral differential equations with variable coefficient and delay: \[ (x(t)-c(t)x(t-\tau (t)))''+a(t)x(t)=f(t,x(t-\delta (t))), \] where \(c(t)\in C(\mathbb {R},\mathbb {R})\) and \(|c(t)|\neq 1\). By employing Krasnoselskii’s fixed-point theorem and properties of the neutral operator \((Ax)(t):=x(t)-c(t)x(t-\tau (t))\), some sufficient conditions for the existence of periodic solutions are established.

Cited in 27 Documents

MSC:

34K13 Periodic solutions to functional-differential equations
34K40 Neutral functional-differential equations
47N20 Applications of operator theory to differential and integral equations

Keywords:

neutral operator; second-order equation; positive periodic solution; two operators; Krasnoselskii’s fixed-point theorem
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References:

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