scholarly journals Existence and uniqueness of periodic solutions for some nonlinear fractional pantograph differential equations with $$\psi $$-Caputo derivative

2021 ◽  
Author(s):  
Soufyane Bouriah ◽  
Djamal Foukrach ◽  
Mouffak Benchohra ◽  
John Graef
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Caputo Derivative ◽  
Existence And Uniqueness ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Coincidence Degree Theory

AbstractThe aim of this paper is to study the existence and uniqueness of periodic solutions for a certain type of nonlinear fractional pantograph differential equation with a $$\psi $$ ψ -Caputo derivative. The proofs are based on the coincidence degree theory of Mawhin. To show the efficiency of the results, some illustrative examples are included.

scholarly journals The Existence and Uniqueness of Periodic Solutions for Some Nonlinearnth-Order Differential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-17
Author(s):  
Qiyuan Zhou ◽  
Shuhua Gong
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Existence And Uniqueness ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Previous Literature ◽  
Coincidence Degree Theory ◽  
Inequality Techniques

The nonlinearnth-order differential equations are considered. By using inequality techniques and coincidence degree theory, some criteria are obtained to guarantee the existence and uniqueness ofT-periodic solutions for the equations. The obtained results are also valid and new for the problem discussed in the previous literature. Moreover, two illustrative examples are provided to illustrate the effectiveness of our results.

scholarly journals Periodic Solutions for a Class of -th Order Functional Differential Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-21 ◽  
Author(s):  
Bing Song ◽  
Lijun Pan ◽  
Jinde Cao
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Functional Differential Equations ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Coincidence Degree Theory ◽  
Existence Of Periodic Solutions ◽  
Functional Differential

We study the existence of periodic solutions forn-th order functional differential equations . Some new results on the existence of periodic solutions of the equations are obtained. Our approach is based on the coincidence degree theory of Mawhin.

ANTI-PERIODIC SOLUTIONS FOR A CLASS OF 2nTH-ORDER NONLINEAR DIFFERENTIAL EQUATIONS WITH DELAYS

2011 ◽  
Vol 04 (04) ◽  
pp. 627-641
Author(s):  
Yongkun Li ◽  
Tianwei Zhang
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Nonlinear Differential Equations ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Coincidence Degree Theory

By applying a fixed point theorem of coincidence degree theory, some criteria are established for the existence of anti-periodic solutions to a class of 2nth-order nonlinear differential equations with delays in the form of [Formula: see text] We extend some recent results to obtain a completely new result. Finally, some examples are given to illustrate our result.

scholarly journals Periodic Solutions for Duffing Typep-Laplacian Equation with Multiple Constant Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
Hong Zhang ◽  
Junxia Meng
Keyword(s):  
Periodic Solutions ◽  
Existence And Uniqueness ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Coincidence Degree Theory ◽  
Laplacian Equation ◽  
Inequality Techniques

Using inequality techniques and coincidence degree theory, new results are provided concerning the existence and uniqueness of periodic solutions for the Duffing typep-Laplacian equation with multiple constant delays of the form(φp(x′(t)))′+Cx′(t)+g0(t,x(t))+∑k=1ngk(t,x(t-τk))=e(t).Moreover, an example is provided to illustrate the effectiveness of the results in this paper.

scholarly journals Multiple Periodic Solutions of a Nonautonomous Plant-Hare Model

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Yongfei Gao ◽  
P. J. Y. Wong ◽  
Y. H. Xia ◽  
Xiaoqing Yuan
Keyword(s):  
Periodic Solutions ◽  
Functional Response ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Coincidence Degree Theory ◽  
New Technique ◽  
Positive Periodic Solutions ◽  
Multiple Periodic Solutions

Based on Mawhin's coincidence degree theory, sufficient conditions are obtained for the existence of at leasttwopositive periodic solutions for a plant-hare model with toxin-determined functional response (nonmonotone). Some new technique is used in this paper, because standard arguments in the literature are not applicable.

scholarly journals 2 N POSITIVE PERIODIC SOLUTIONS TO N SPECIES NON‐AUTONOMOUS LOTKA‐VOLTERRA UNIDIRECTIONAL FOOD CHAINS WITH HARVESTING TERMS

2010 ◽  
Vol 15 (3) ◽  
pp. 313-326 ◽  
Author(s):  
Yongkun Li ◽  
Kaihong Zhao
Keyword(s):  
Periodic Solutions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Continuation Theorem ◽  
Coincidence Degree Theory ◽  
Food Chains ◽  
Positive Periodic Solutions ◽  
Mawhin Continuation Theorem

By using the Mawhin continuation theorem of coincidence degree theory and some results on inequalities, we establish the existence of 2 n positive periodic solutions for n species non‐autonomous Lotka‐Volterra unidirectional food chains with harvesting terms. Two examples are given to illustrate the effectiveness of our results.

scholarly journals Multiple Positive Periodic Solutions for a Gilpin-Ayala Competition Predator-Prey System with Harvesting Terms

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
Yongzhi Liao ◽  
Yongkun Li ◽  
Xiaoyan Dou
Keyword(s):  
Periodic Solutions ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Continuation Theorem ◽  
Coincidence Degree Theory ◽  
Positive Periodic Solutions ◽  
Mawhin’S Continuation Theorem ◽  
Predator Prey ◽  
Prey System

By applying Mawhin’s continuation theorem of coincidence degree theory, we study the existence of multiple positive periodic solutions for a Gilpin-Ayala competition predator-prey system with harvesting terms and obtain some sufficient conditions for the existence of multiple positive periodic solutions for the system under consideration. The result of this paper is completely new. An example is employed to illustrate our result.

scholarly journals Multiple Periodic Solutions of Generalized Gause-Type Predator-Prey Systems with Nonmonotonic Numerical Responses and Impulse

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Zhenguo Luo ◽  
Liping Luo ◽  
Yunhui Zeng
Keyword(s):  
Periodic Solutions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Continuation Theorem ◽  
Coincidence Degree Theory ◽  
Sufficient Condition ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Multiple Periodic Solutions

We consider an impulsive periodic generalized Gause-type predator-prey model with nonmonotonic numerical responses. Using the continuation theorem of coincidence degree theory, we present an easily verifiable sufficient condition on the existence of multiple periodic solutions. As corollaries, some applications are listed. In particular, our results extend and improve some known criteria.

Existence of Periodic Solutions to a Class of Environmental Mathematical Model

2012 ◽  
Vol 518-523 ◽  
pp. 1540-1543
Author(s):  
Jun Yi Yin
Keyword(s):  
Mathematical Model ◽  
Periodic Solutions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Coincidence Degree Theory ◽  
Number Of Species ◽  
Existence Of Periodic Solutions

This paper has studied a class of environmental mathematical model by using the coincidence degree theory, verified the existence of periodic solutions of the system to meet certain conditions, and revealed a relationship between a number of species in the system and pollution.

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