Asymptotic integration of second-order nonlinear differential equations via principal and nonprincipal solutions

Ertem, Türker; Zafer, A.

doi:10.1016/j.amc.2012.11.094

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Cited by 8 publications

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“…In the mathematical literature there are many existence results on singular differential equations [3][4][5][6][7][8]. We are mainly motivated by [1] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

The Existence of Positive Solutions of Singular Initial-Value Problem for Second Order Differential Equations-2

Aslanov¹

2020

Communications in Advanced Mathematical Sciences

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We consider the singular initial value problem for the second order differential equation. We interested in the existence of positive solutions and proved an easily applicable theorem on the existence of positive solutions to initial-value problems for second-order nonlinear singular differential equations. The previously established result on the existence of positive solution by Agarwal and O'Regan is not easy for the applications due to very complex definition of a new function and their properties in the statement of their theorem. We used the Lebesgue dominated convergence theorem and the Schauder-Tychonoff theorem in the proof of the main result. The main result can be easily applied for the singular and regular type of problems.

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“…In the mathematical literature there are many existence results on singular differential equations [3][4][5][6][7][8]. We are mainly motivated by [1] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

The Existence of Positive Solutions of Singular Initial-Value Problem for Second Order Differential Equations-2

Aslanov¹

2020

Communications in Advanced Mathematical Sciences

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A Note on The Asymptotic Solution of Second Order Nonlinear Differential Equation

Aslanov

2022

Mediterr. J. Math.

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On the existence of monotone positive solutions of second order differential equations

Aslanov

2016

Monatsh Math

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Asymptotic integration of second-order nonlinear differential equations via principal and nonprincipal solutions

Cited by 8 publications

References 5 publications

The Existence of Positive Solutions of Singular Initial-Value Problem for Second Order Differential Equations-2

The Existence of Positive Solutions of Singular Initial-Value Problem for Second Order Differential Equations-2

A Note on The Asymptotic Solution of Second Order Nonlinear Differential Equation

On the existence of monotone positive solutions of second order differential equations

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