On the existence of periodic solutions to a fourth-order -Laplacian differential equation with a deviating argument

2010 ◽  
Vol 11 (3) ◽  
pp. 1660-1669 ◽  
Author(s):  
Zhengxin Wang ◽  
Longxia Qian ◽  
Shiping Lu
Keyword(s):  
Differential Equation ◽  
Periodic Solutions ◽  
Fourth Order ◽  
Deviating Argument ◽  
Existence Of Periodic Solutions

Positive periodic solutions for singular fourth-order differential equations with a deviating argument

2018 ◽  
Vol 148 (3) ◽  
pp. 605-617 ◽  
Author(s):  
Fanchao Kong ◽  
Zaitao Liang
Keyword(s):  
Differential Equation ◽  
Periodic Solutions ◽  
Fourth Order ◽  
Order Differential Equation ◽  
Positive Periodic Solutions ◽  
Mawhin’S Continuation Theorem ◽  
Deviating Argument ◽  
Small Force ◽  
Image Position ◽  
Fourth Order Differential Equation

In this paper, we study the singular fourth-order differential equation with a deviating argument:By using Mawhin's continuation theorem and some analytic techniques, we establish some criteria to guarantee the existence of positive periodic solutions. The significance of this paper is that g has a strong singularity at x = 0 and satisfies a small force condition at x = ∞, which is different from the known ones in the literature.

scholarly journals Periodic Solutions of Duffing Equation with an Asymmetric Nonlinearity and a Deviating Argument

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Zaihong Wang ◽  
Jin Li ◽  
Tiantian Ma
Keyword(s):  
Differential Equation ◽  
Periodic Solutions ◽  
Order Differential Equation ◽  
Sufficient Conditions ◽  
Second Order ◽  
Duffing Equation ◽  
Deviating Argument ◽  
Second Order Differential Equation ◽  
Existence Of Periodic Solutions ◽  
The Given

We study the existence of periodic solutions of the second-order differential equationx′′+ax+-bx-+g(x(t-τ))=p(t), wherea,bare two constants satisfying1/a+1/b=2/n,n∈N,τis a constant satisfying0≤τ<2π,g,p:R→Rare continuous, andpis2π-periodic. When the limitslimx→±∞g(x)=g(±∞)exist and are finite, we give some sufficient conditions for the existence of2π-periodic solutions of the given equation.

scholarly journals Periodic solutions for periodic second-order differential equations with variable potentials

2018 ◽  
Vol 24 (2) ◽  
pp. 127-137
Author(s):  
Jaume Llibre ◽  
Ammar Makhlouf
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Order Differential Equation ◽  
Sufficient Conditions ◽  
Second Order ◽  
Second Order Differential Equations ◽  
Second Order Differential Equation ◽  
Existence Of Periodic Solutions

Abstract We provide sufficient conditions for the existence of periodic solutions of the second-order differential equation with variable potentials {-(px^{\prime})^{\prime}(t)-r(t)p(t)x^{\prime}(t)+q(t)x(t)=f(t,x(t))} , where the functions {p(t)>0} , {q(t)} , {r(t)} and {f(t,x)} are {\mathcal{C}^{2}} and T-periodic in the variable t.

Periodic Solutions for a Class of Functional Differential Equations with State-Dependent Delay Close to Zero

2003 ◽  
Vol 13 (06) ◽  
pp. 807-841 ◽  
Author(s):  
R. Ouifki ◽  
M. L. Hbid
Keyword(s):  
Differential Equation ◽  
Hopf Bifurcation ◽  
Periodic Solutions ◽  
Functional Differential Equations ◽  
Delay Equation ◽  
Constant Delay ◽  
State Dependent ◽  
State Dependent Delay ◽  
Existence Of Periodic Solutions ◽  
Functional Differential

The purpose of the paper is to prove the existence of periodic solutions for a functional differential equation with state-dependent delay, of the type [Formula: see text] Transforming this equation into a perturbed constant delay equation and using the Hopf bifurcation result and the Poincaré procedure for this last equation, we prove the existence of a branch of periodic solutions for the state-dependent delay equation, bifurcating from r ≡ 0.

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