scholarly journals Existence for Singular Periodic Problems: A Survey of Recent Results

2013 ◽  
Vol 2013 ◽  
pp. 1-17 ◽  
Author(s):  
Jifeng Chu ◽  
Juntao Sun ◽  
Patricia J. Y. Wong
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Impulsive Differential Equations ◽  
Differential Systems ◽  
Singular Differential Equations ◽  
Periodic Problems ◽  
Existence Of Periodic Solutions

We present a survey on the existence of periodic solutions of singular differential equations. In particular, we pay our attention to singular scalar differential equations, singular damped differential equations, singular impulsive differential equations, and singular differential systems.

scholarly journals Variational Approach to Impulsive Differential Equations with Singular Nonlinearities

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Naima Daoudi-Merzagui ◽  
Abdelkader Boucherif
Keyword(s):  
Differential Equations ◽  
Variational Method ◽  
Periodic Solutions ◽  
Variational Approach ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Second Order ◽  
Second Order Differential Equations ◽  
Singular Nonlinearities ◽  
Existence Of Periodic Solutions

We discuss the existence of periodic solutions for nonautonomous second order differential equations with singular nonlinearities. Simple sufficient conditions that enable us to obtain many distinct periodic solutions are provided. Our approach is based on a variational method.

CONTINUATION THEOREMS FOR AMBROSETTI-PRODI TYPE PERIODIC PROBLEMS

2000 ◽  
Vol 02 (01) ◽  
pp. 87-126 ◽  
Author(s):  
JEAN MAWHIN ◽  
CARLOTA REBELO ◽  
FABIO ZANOLIN
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Periodic Solutions ◽  
A Priori ◽  
Nonlinear Ordinary Differential Equations ◽  
Type Problem ◽  
Normed Spaces ◽  
A Priori Bounds ◽  
Periodic Problems ◽  
Existence Of Periodic Solutions

We study the existence of periodic solutions u(·) for a class of nonlinear ordinary differential equations depending on a real parameter s and obtain the existence of closed connected branches of solution pairs (u, s) to various classes of problems, including some cases, like the superlinear one, where there is a lack of a priori bounds. The results are obtained as a consequence of a new continuation theorem for the coincidence equation Lu=N(u, s) in normed spaces. Among the applications, we discuss also an example of existence of global branches of periodic solutions for the Ambrosetti–Prodi type problem u″+g(u)=s+ p(t), with g satisfying some asymmetric conditions.

scholarly journals Applications of Schauder’s Fixed Point Theorem to Semipositone Singular Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Zhongwei Cao ◽  
Chengjun Yuan ◽  
Xiuling Li
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Schauder’S Fixed Point Theorem ◽  
Singular Differential Equations ◽  
Schauder's Fixed Point Theorem ◽  
Existence Of Periodic Solutions ◽  
Weak Singularities

We study the existence of positive periodic solutions of second-order singular differential equations. The proof relies on Schauder’s fixed point theorem. Our results generalized and extended those results contained in the studies by Chu and Torres (2007) and Torres (2007) . In some suitable weak singularities, the existence of periodic solutions may help.

scholarly journals RETRACTED ARTICLE: PERIODIC SOLUTIONS OF SECOND ORDER IMPULSIVE DIFFERENTIAL EQUATIONS AT RESONANCE VIA VARIATIONAL APPROACH

2014 ◽  
Vol 19 (5) ◽  
pp. 664-675 ◽  
Author(s):  
Jin Li ◽  
Jianlin Luo ◽  
Zaihong Wang
Keyword(s):  
Differential Equations ◽  
Variational Method ◽  
Periodic Solutions ◽  
Variational Approach ◽  
Impulsive Differential Equations ◽  
Second Order ◽  
Type Condition ◽  
At Resonance ◽  
Retracted Article ◽  
Existence Of Periodic Solutions

In this paper, we study the existence of periodic solutions of second order impulsive dierential equations at resonance. We prove the existence of periodic solutions under a generalized Landesman{Lazer type condition by using variational method.

A new Ф-generalized quasi metric space with some fixed point results and applications

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3157-3172
Author(s):  
Mujahid Abbas ◽  
Bahru Leyew ◽  
Safeer Khan
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fixed Points ◽  
Periodic Solutions ◽  
Metric Space ◽  
Delay Differential Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Existence Of Periodic Solutions ◽  
Delay Differential

In this paper, the concept of a new ?-generalized quasi metric space is introduced. A number of well-known quasi metric spaces are retrieved from ?-generalized quasi metric space. Some general fixed point theorems in a ?-generalized quasi metric spaces are proved, which generalize, modify and unify some existing fixed point theorems in the literature. We also give applications of our results to obtain fixed points for contraction mappings in the domain of words and to prove the existence of periodic solutions of delay differential equations.

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