Polynomial solution of singular differential equations using Weighted Sobolev gradients

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.

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Fuzzy linear singular differential equations under granular differentiability concept

Fuzzy Sets and Systems ◽

10.1016/j.fss.2021.01.003 ◽

2021 ◽

Author(s):

Marzieh Najariyan ◽

Naser Pariz ◽

Ho Vu

Keyword(s):

Differential Equations ◽

Singular Differential Equations

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

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.40-41.149 ◽

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.

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Lucas Polynomial solution of Nonlinear Differential Equations with Variable Delay

Hacettepe Journal of Mathematics and Statistics ◽

10.15672/hujms.460975 ◽

2019 ◽

pp. 1-12 ◽

Cited By ~ 1

Author(s):

Sevin Gümgüm ◽

Nurcan Baykuş Savaşaneril ◽

Ömür Kıvanç Kürkçü ◽

Mehmet Sezer

Keyword(s):

Differential Equations ◽

Nonlinear Differential Equations ◽

Polynomial Solution ◽

Variable Delay

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PERIODIC SOLUTIONS OF SINGULAR DIFFERENTIAL EQUATIONS WITH SIGN-CHANGING POTENTIAL

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972710001607 ◽

2010 ◽

Vol 82 (3) ◽

pp. 437-445 ◽

Cited By ~ 10

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.

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