scholarly journals Existence of nontrivial periodic solutions for first order functional differential equations

2005 ◽  
Vol 18 (1) ◽  
pp. 101-107 ◽  
Author(s):  
Shugui Kang ◽  
Guang Zhang
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Functional Differential Equations ◽  
First Order ◽  
Nontrivial Periodic Solutions ◽  
Functional Differential

Periodic solutions of ordinary differential equations with one-sided growth restrictions

1978 ◽  
Vol 82 (1-2) ◽  
pp. 95-106 ◽  
Author(s):  
J. Mawhin ◽  
W. Walter
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Functional Differential Equations ◽  
First Order ◽  
Asymptotic Nature ◽  
Special Cases ◽  
Existence Of Periodic Solutions ◽  
Growth Restrictions ◽  
Functional Differential ◽  
The Right

SynopsisThe existence of periodic solutions is proved for first order vector ordinary and functional differential equations when the right-hand side satisfies a one-sided growth restriction of Wintner type together with some conditions of asymptotic nature. Special cases in the line of Landesman-Lazer and of Winston are explicited.

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).

Periodic solutions for functional differential equations with sign-changing nonlinearities

2010 ◽  
Vol 140 (3) ◽  
pp. 597-616 ◽  
Author(s):  
John R. Graef ◽  
Lingju Kong
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Eigenvalue Problems ◽  
Functional Differential Equations ◽  
Degree Theory ◽  
Topological Degree Theory ◽  
First Order ◽  
Functional Differential ◽  
Linear Integral ◽  
The Relationship

We establish some eigenvalue criteria for the existence of non-trivial T-periodic solutions of a class of first-order functional differential equations with a nonlinearity f(x). The nonlinear term f(x) can take negative values and may be unbounded from below. Conditions are determined by the relationship between the behaviour of the quotient f(x)/x for x near 0 and ±∞ and the smallest positive characteristic value of an associated linear integral operator. This linear operator plays a key role in the proofs of the results and its construction is non-trivial. Applications to related eigenvalue problems are also discussed. The analysis mainly relies on the topological degree theory.

Sign in / Sign up

Export Citation Format

Share Document