Three periodic solutions for a nonlinear first order functional differential equation

2010 ◽  
Vol 216 (8) ◽  
pp. 2450-2456 ◽  
Author(s):  
Seshadev Padhi ◽  
Shilpee Srivastava ◽  
Smita Pati
Keyword(s):  
Differential Equation ◽  
Periodic Solutions ◽  
Functional Differential Equation ◽  
First Order ◽  
Functional Differential

scholarly journals One-Signed Periodic Solutions of First-Order Functional Differential Equations with a Parameter

2011 ◽  
Vol 2011 ◽  
pp. 1-11 ◽  
Author(s):  
Ruyun Ma ◽  
Yanqiong Lu
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Periodic Function ◽  
Periodic Solutions ◽  
Functional Differential Equation ◽  
Functional Differential Equations ◽  
Global Bifurcation ◽  
Periodic Functions ◽  
First Order ◽  
Functional Differential

We study one-signed periodic solutions of the first-order functional differential equationu'(t)=-a(t)u(t)+λb(t)f(u(t-τ(t))),t∈Rby using global bifurcation techniques. Wherea,b∈C(R,[0,∞))areω-periodic functions with∫0ωa(t)dt>0,∫0ωb(t)dt>0,τis a continuousω-periodic function, andλ>0is a parameter.f∈C(R,R)and there exist two constantss2<0<s1such thatf(s2)=f(0)=f(s1)=0,f(s)>0fors∈(0,s1)∪(s1,∞)andf(s)<0fors∈(-∞,s2)∪(s2,0).

scholarly journals Oscillations of a first order functional differential equation

1977 ◽  
Vol 17 (1) ◽  
pp. 91-95 ◽  
Author(s):  
Alexander Tomaras
Keyword(s):  
Differential Equation ◽  
Functional Differential Equation ◽  
First Order ◽  
Functional Differential

Oscillation results are obtained for a first order functional differential equation, by transforming it to an equation for which oscillatory information exists in the literature already.

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