Infinitely many periodic solutions for fourth-order impulsive differential equation with oscillatory nonlinear term

2020 ◽  
Vol 50 (5) ◽  
pp. 1833-1851
Author(s):  
Suiming Shang ◽  
Yue Yue ◽  
Zhanbing Bai
Keyword(s):  
Differential Equation ◽  
Periodic Solutions ◽  
Fourth Order ◽  
Impulsive Differential Equation ◽  
Nonlinear Term ◽  
Infinitely Many Periodic Solutions

scholarly journals Nontrivial Solutions for a Boundary Value Problem of nth-Order Impulsive Differential Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Jiafa Xu ◽  
Zhongli Wei
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Impulsive Differential Equation ◽  
Nonlinear Term ◽  
Boundary Value ◽  
Degree Theory ◽  
Impulsive Effects ◽  
Nontrivial Solutions

We study the existence of nontrivial solutions for nth-order boundary value problem with impulsive effects. We utilize Leray-Schauder degree theory to establish our main results. Furthermore, our nonlinear term f is allowed to grow superlinearly and sublinearly.

scholarly journals The Integrability and Existence of Periodic Solutions on a First-Order Nonlinear Differential Equation with a Polynomial Nonlinear Term

2012 ◽  
Vol 2012 ◽  
pp. 1-26
Author(s):  
Ni Hua ◽  
Tian Li-Xin
Keyword(s):  
Differential Equation ◽  
Periodic Solutions ◽  
Nonlinear Differential Equation ◽  
Nonlinear Term ◽  
Order Differential Equation ◽  
First Order ◽  
Order Nonlinear Differential Equation ◽  
Existence Of Periodic Solutions ◽  
The Stability

This paper deals with a first-order differential equation with a polynomial nonlinear term. The integrability and existence of periodic solutions of the equation are obtained, and the stability of periodic solutions of the equation is derived.

scholarly journals Existence of Infinitely Many Periodic Solutions for Perturbed Semilinear Fourth-Order Impulsive Differential Inclusions

2016 ◽  
Vol 2016 ◽  
pp. 1-12
Author(s):  
Massimiliano Ferrara ◽  
Giuseppe Caristi ◽  
Amjad Salari
Keyword(s):  
Critical Point ◽  
Periodic Solutions ◽  
Differential Inclusion ◽  
Point Theorem ◽  
Fourth Order ◽  
Differential Inclusions ◽  
Critical Point Theorem ◽  
Impulsive Differential Inclusions ◽  
Two Parameters ◽  
Infinitely Many Periodic Solutions

This paper discusses the existence of infinitely many periodic solutions for a semilinear fourth-order impulsive differential inclusion with a perturbed nonlinearity and two parameters. The approach is based on a critical point theorem for nonsmooth functionals.

scholarly journals Some Existence Results for High Order Fractional Impulsive Differential Equation on Infinite Interval

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Zhaocai Hao ◽  
Tian Wang
Keyword(s):  
Differential Equation ◽  
Fixed Points ◽  
Impulsive Differential Equation ◽  
Nonlinear Term ◽  
Existence Of Solutions ◽  
Existence Results ◽  
High Order ◽  
Infinite Interval ◽  
Derivative Operator ◽  
Lower Order Derivative

In this paper, we consider the high order impulsive differential equation on infinite interval D 0 + α u t + f t , u t , J 0 + β u t , D 0 + α − 1 u t = 0 ,   t ∈ 0 , ∞ ∖ t k k = 1 m △ u t k = I k u t k ,   t = t k , k = 1 , … , m u 0 = u ′ 0 = ⋯ = u n − 2 0 = 0 , D 0 + α − 1 u ∞ = u 0 By applying Schauder fixed points and Altman fixed points, we obtain some new results on the existence of solutions. The nonlinear term of the equation contains fractional integral operator J β u t and lower order derivative operator D 0 + α − 1 u t . An example is presented to illustrate our results.

EXACT HETEROCLINIC CYCLE FAMILY AND QUASI-PERIODIC SOLUTIONS FOR THE THREE-DIMENSIONAL SYSTEMS DETERMINED BY CHAZY CLASS IX

2011 ◽  
Vol 21 (05) ◽  
pp. 1357-1367 ◽  
Author(s):  
JIBIN LI ◽  
XIAOHUA ZHAO
Keyword(s):  
Dynamical System ◽  
Differential Equation ◽  
Periodic Solutions ◽  
Level Set ◽  
Three Dimensional ◽  
Heteroclinic Cycle ◽  
Dimensional System ◽  
Three Dimensional System ◽  
Infinitely Many Periodic Solutions

For differential equation in the Chazy class IX, their corresponding three-dimensional system is studied in this paper by using dynamical system methods and Cosgrove's results. In a level set, the exact explicit parametric representations of a heteroclinic cycle family and uncountably infinitely many periodic solutions as well as quasi-periodic solutions, are all obtained.

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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