scholarly journals EXISTENCE AND MULTIPLICITY OF POSITIVE PERIODIC SOLUTIONS FOR A CLASS OF SECOND ORDER DAMPED FUNCTIONAL DIFFERENTIAL EQUATIONS WITH MULTIPLE DELAYS

2020 ◽  
Vol 0 (0) ◽  
pp. 0-0
Author(s):  
Ping Liu ◽  
◽  
Yonghong Fan ◽  
Linlin Wang
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Functional Differential Equations ◽  
Second Order ◽  
Multiple Delays ◽  
Positive Periodic Solutions ◽  
Existence And Multiplicity ◽  
Functional Differential

On positive periodic solutions of linear second order functional differential equations

2017 ◽  
Vol 24 (1) ◽  
pp. 29-39 ◽  
Author(s):  
Eugene I. Bravyi
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Periodic Solutions ◽  
Periodic Boundary ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Second Order ◽  
Periodic Boundary Value Problem ◽  
Positive Periodic Solutions ◽  
Functional Differential

AbstractThe periodic boundary value problem for linear second order functional differential equations is considered. Sharp sufficient conditions for the positiveness of solutions are obtained.

scholarly journals On the Existence of Positive Periodic Solutions for Second-Order Functional Differential Equations with Multiple Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Qiang Li ◽  
Yongxiang Li
Keyword(s):  
Periodic Solutions ◽  
Functional Differential Equations ◽  
Index Theory ◽  
Second Order ◽  
Multiple Delays ◽  
First Eigenvalue ◽  
Fixed Point Index Theory ◽  
Existence Conditions ◽  
Functional Differential ◽  
Periodic Boundary Problem

The existence results of positiveω-periodic solutions are obtained for the second-order functional differential equation with multiple delaysu″(t)+a(t)u(t)=f(t,u(t),u(t−τ1(t)),…,u(t−τn(t))), wherea(t)∈C(ℝ)is a positiveω-periodic function,f:ℝ×[0,+∞)n+1→[0,+∞)is a continuous function which isω-periodic int, andτ1(t),…,τn(t)∈C(ℝ,[0,+∞))areω-periodic functions. The existence conditions concern the first eigenvalue of the associated linear periodic boundary problem. Our discussion is based on the fixed-point index theory in cones.

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