Puiseux Solutions of Singular Differential Equations

2000 ◽  
pp. 129-145 ◽  
Author(s):  
José Manuel Aroca
Keyword(s):  
Differential Equations ◽  
Singular Differential Equations

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.

A Existence Theory for Positive Solutions to Superlinear Repulsive Singular Differential Equations with Impulse Effects

2010 ◽  
Vol 40-41 ◽  
pp. 149-155
Author(s):  
Zhang Xiao Ying ◽  
Guan Li Hong
Keyword(s):  
Periodic Solution ◽  
Differential Equations ◽  
Singular Perturbation ◽  
Positive Solutions ◽  
Existence Theory ◽  
Singular Differential Equations ◽  
Perturbation Problem ◽  
Nonlinear Alternative

In this paper, we study positive solutions to the repulsive singular perturbation Hill equations with impulse effects. It is proved that such a perturbation problem has at least one positive impulsive periodic solution by a nonlinear alternative of Leray--Schauder.

scholarly journals PERIODIC SOLUTIONS OF SINGULAR DIFFERENTIAL EQUATIONS WITH SIGN-CHANGING POTENTIAL

2010 ◽  
Vol 82 (3) ◽  
pp. 437-445 ◽  
Author(s):  
JIFENG CHU ◽  
ZIHENG ZHANG
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Second Order ◽  
Schauder’S Fixed Point Theorem ◽  
Positive Periodic Solutions ◽  
Singular Differential Equations ◽  
Attractive Case

AbstractIn this paper we study the existence of positive periodic solutions to second-order singular differential equations with the sign-changing potential. Both the repulsive case and the attractive case are studied. The proof is based on Schauder’s fixed point theorem. Recent results in the literature are generalized and significantly improved.

Singular Differential Equations in Banach Spaces

2002 ◽  
pp. 337-430
Author(s):  
Nikolay Sidorov ◽  
Boris Loginov ◽  
Aleksandr Sinitsyn ◽  
Michail Falaleev
Keyword(s):  
Differential Equations ◽  
Banach Spaces ◽  
Singular Differential Equations

A class of nonlinear singular differential equations

2019 ◽  
Vol 22 (6) ◽  
pp. 991-1007 ◽  
Author(s):  
Abdelkader Benzidane ◽  
Zoubir Dahmani
Keyword(s):  
Differential Equations ◽  
Singular Differential Equations

scholarly journals A Review on a Class of Second Order Nonlinear Singular BVPs

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1045
Author(s):  
Amit K. Verma ◽  
Biswajit Pandit ◽  
Lajja Verma ◽  
Ravi P. Agarwal
Keyword(s):  
Exact Solution ◽  
Differential Equations ◽  
Real Life ◽  
Monotone Iterative Technique ◽  
Singular Boundary ◽  
Singular Boundary Value Problems ◽  
Numerical Techniques ◽  
Singular Differential Equations ◽  
Monotone Iterative ◽  
Life Problems

Several real-life problems are modeled by nonlinear singular differential equations. In this article, we study a class of nonlinear singular differential equations, explore its various aspects, and provide a detailed literature survey. Nonlinear singular differential equations are not easy to solve and their exact solution does not exist in most cases. Since the exact solution does not exist, it is natural to look for the existence of the analytical solution and numerical solution. In this survey, we focus on both aspects of nonlinear singular boundary value problems (SBVPs) and cover different analytical and numerical techniques which are developed to deal with a class of nonlinear singular differential equations − ( p ( x ) y ′ ( x ) ) ′ = q ( x ) f ( x , y , p y ′ ) for x ∈ ( 0 , b ) , subject to suitable initial and boundary conditions. The monotone iterative technique has also been briefed as it gained a lot of attention during the last two decades and it has been merged with most of the other existing techniques. A list of SBVPs is also provided which will be of great help to researchers working in this area.

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