Positive Periodic Solutions for a Kind of Second-Order Neutral Differential Equations with Variable Coefficient and Delay

Positive Periodic Solutions for a Kind of Second-Order Neutral Differential Equations with... In this article, we discuss a type of second-order neutral differential equations with variable coefficient and delay: $$\begin{aligned} (x(t)-c(t)x(t-\tau (t)))''+a(t)x(t)=f(t,x(t-\delta (t))), \end{aligned}$$ ( x ( t ) - c ( t ) x ( t - τ ( t ) ) ) ′ ′ + a ( t ) x ( t ) = f ( t , x ( t - δ ( t ) ) ) , where $$c(t)\in C({\mathbb {R}},{\mathbb {R}})$$ c ( t ) ∈ C ( R , R ) and $$|c(t)|\ne 1$$ | c ( t ) | ≠ 1 . By employing Krasnoselskii’s fixed-point theorem and properties of the neutral operator $$(Ax)(t):=x(t)-c(t)x(t-\tau (t))$$ ( A x ) ( t ) : = x ( t ) - c ( t ) x ( t - τ ( t ) ) , some sufficient conditions for the existence of periodic solutions are established. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mediterranean Journal of Mathematics Springer Journals

Positive Periodic Solutions for a Kind of Second-Order Neutral Differential Equations with Variable Coefficient and Delay

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Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer International Publishing AG, part of Springer Nature
Subject
Mathematics; Mathematics, general
ISSN
1660-5446
eISSN
1660-5454
D.O.I.
10.1007/s00009-018-1184-y
Publisher site
See Article on Publisher Site

Abstract

In this article, we discuss a type of second-order neutral differential equations with variable coefficient and delay: $$\begin{aligned} (x(t)-c(t)x(t-\tau (t)))''+a(t)x(t)=f(t,x(t-\delta (t))), \end{aligned}$$ ( x ( t ) - c ( t ) x ( t - τ ( t ) ) ) ′ ′ + a ( t ) x ( t ) = f ( t , x ( t - δ ( t ) ) ) , where $$c(t)\in C({\mathbb {R}},{\mathbb {R}})$$ c ( t ) ∈ C ( R , R ) and $$|c(t)|\ne 1$$ | c ( t ) | ≠ 1 . By employing Krasnoselskii’s fixed-point theorem and properties of the neutral operator $$(Ax)(t):=x(t)-c(t)x(t-\tau (t))$$ ( A x ) ( t ) : = x ( t ) - c ( t ) x ( t - τ ( t ) ) , some sufficient conditions for the existence of periodic solutions are established.

Journal

Mediterranean Journal of MathematicsSpringer Journals

Published: May 31, 2018

References

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