Periodic solutions for a fourth-order -Laplacian differential equation with a deviating argument

2008 ◽  
Vol 69 (5-6) ◽  
pp. 1710-1718 ◽  
Author(s):  
Jin Shan ◽  
Lu Shiping
Keyword(s):  
Differential Equation ◽  
Periodic Solutions ◽  
Fourth Order ◽  
Deviating Argument

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.

Multibump periodic travelling waves in suspension bridges

1998 ◽  
Vol 128 (3) ◽  
pp. 631-659 ◽  
Author(s):  
L. A. Peletier ◽  
W. C. Troy
Keyword(s):  
Differential Equation ◽  
Periodic Solutions ◽  
Nonlinear Differential Equation ◽  
Fourth Order ◽  
Infinite Number ◽  
Travelling Waves ◽  
Suspension Bridges ◽  
Shooting Argument ◽  
Different Types ◽  
Countably Infinite

We investigate different types of periodic solutions of a fourth-order, nonlinear differential equation, which has been proposed as a model for travelling waves in suspension bridges. We develop a shooting argument, which enables us to prove the existence of two families of multibump periodic solutions, each containing a countably infinite number of different solutions

Existence of positive periodic solutions for fourth-order nonlinear neutral differential equations with variable delay

2014 ◽  
Vol 0 (0) ◽  
Author(s):  
Abdelouaheb Ardjouni ◽  
Ali Rezaiguia ◽  
Ahcene Djoudi
Keyword(s):  
Differential Equation ◽  
Periodic Solutions ◽  
Fourth Order ◽  
Main Tool ◽  
The Other ◽  
Variable Delay ◽  
Positive Periodic Solutions ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Completely Continuous ◽  
Neutral Differential Equations

Abstract.In this article we study the existence of positive periodic solutions for a fourth-order nonlinear neutral differential equation with variable delay. The main tool employed here is the Krasnoselskii's fixed point theorem dealing with a sum of two mappings, one is a contraction and the other one is completely continuous.

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