# Periodic solutions for some double-delayed differential equations

Periodic solutions for some double-delayed differential equations We prove the existence of positive $$\omega$$ ω -periodic solutions for the double-delayed differential equation \begin{aligned} x^{\prime }(t)-a(t)g(x(t))x(t)=-\lambda (b(t)f(x(t-\tau (t))+c(t)h(x(t-\nu (t))), \end{aligned} x ′ ( t ) - a ( t ) g ( x ( t ) ) x ( t ) = - λ ( b ( t ) f ( x ( t - τ ( t ) ) + c ( t ) h ( x ( t - ν ( t ) ) ) , where $$\lambda$$ λ is a positive parameter, $$a,b,c,\tau ,\nu \in C(\mathbb {R}, \mathbb {R})$$ a , b , c , τ , ν ∈ C ( R , R ) are $$\omega$$ ω -periodic functions with $$a,b\ge 0,a,b\not \equiv 0,f,g,h\in C([0,\infty ),\mathbb {R})$$ a , b ≥ 0 , a , b ≢ 0 , f , g , h ∈ C ( [ 0 , ∞ ) , R ) with $$g>0$$ g > 0 on $$(0,\infty ),$$ ( 0 , ∞ ) , $$\ h$$ h is bounded, f is either superlinear or sublinear at $$\infty$$ ∞ and could change sign. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

# Periodic solutions for some double-delayed differential equations

, Volume 21 (1) – Feb 10, 2016
7 pages

/lp/springer_journal/periodic-solutions-for-some-double-delayed-differential-equations-AImEv00XlO
Publisher
Springer International Publishing
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-016-0399-z
Publisher site
See Article on Publisher Site

### Abstract

We prove the existence of positive $$\omega$$ ω -periodic solutions for the double-delayed differential equation \begin{aligned} x^{\prime }(t)-a(t)g(x(t))x(t)=-\lambda (b(t)f(x(t-\tau (t))+c(t)h(x(t-\nu (t))), \end{aligned} x ′ ( t ) - a ( t ) g ( x ( t ) ) x ( t ) = - λ ( b ( t ) f ( x ( t - τ ( t ) ) + c ( t ) h ( x ( t - ν ( t ) ) ) , where $$\lambda$$ λ is a positive parameter, $$a,b,c,\tau ,\nu \in C(\mathbb {R}, \mathbb {R})$$ a , b , c , τ , ν ∈ C ( R , R ) are $$\omega$$ ω -periodic functions with $$a,b\ge 0,a,b\not \equiv 0,f,g,h\in C([0,\infty ),\mathbb {R})$$ a , b ≥ 0 , a , b ≢ 0 , f , g , h ∈ C ( [ 0 , ∞ ) , R ) with $$g>0$$ g > 0 on $$(0,\infty ),$$ ( 0 , ∞ ) , $$\ h$$ h is bounded, f is either superlinear or sublinear at $$\infty$$ ∞ and could change sign.

### Journal

PositivitySpringer Journals

Published: Feb 10, 2016

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