Monotone positive solutions for a class of second-order nonlinear differential equations

Ertem, Türker; Zafer, A.

doi:10.1016/j.cam.2013.04.020

Cited by 14 publications

(3 citation statements)

References 5 publications

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“…By Krasnoselskii fixed point theorem on cone compression and expansion, Zima [46] studied the existence of positive solutions for the above boundary value problem when f : (0, +∞) × [0, +∞) → [0, +∞) is continuous. In particular, by using suitable growth condition and fixed point theorem, Yin [33], Constantin [4], Ertem and Zafer [8] presented the existence and asymptotic behavior of positive solutions for an extended version of Eq. (6), respectively.…”

Section: Introductionmentioning

confidence: 99%

Solvability and asymptotic properties for an elliptic geophysical fluid flows model in a planar exterior domain

Zhang

Liu

et al. 2021

NAMC

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In this paper, we study the solvability and asymptotic properties of a recently derived gyre model of nonlinear elliptic Schrödinger equation arising from the geophysical fluid flows. The existence theorems and the asymptotic properties for radial positive solutions are established due to space theory and analytical techniques, some special cases and specific examples are also given to describe the applicability of model in gyres of geophysical fluid flows.

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Section: Introductionmentioning

confidence: 99%

Solvability and asymptotic properties for an elliptic geophysical fluid flows model in a planar exterior domain

Zhang

Liu

et al. 2021

NAMC

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“…The weak point of the papers of Demidovich and Iseki consists of the fact that they demonstrate the boundedness of monotonous solutions, without specifying whether such solutions exist. Regarding the existence of monotonic solutions of differential equations, important results were obtained by Rovderová [3], Tóthová and Palumbíny [4], Rovder [5], Li and Fan [6], Yin [7], Ertem and Zafer [8], Aslanov [9], Chu [10], and Sanhan et al [11].…”

Section: Introductionmentioning

confidence: 99%

An Application of the Fixed Point Theory to the Study of Monotonic Solutions for Systems of Differential Equations

Branga

Olaru

2020

Mathematics

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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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Monotone positive solutions for a class of second-order nonlinear differential equations

Cited by 14 publications

References 5 publications

Solvability and asymptotic properties for an elliptic geophysical fluid flows model in a planar exterior domain

Solvability and asymptotic properties for an elliptic geophysical fluid flows model in a planar exterior domain

An Application of the Fixed Point Theory to the Study of Monotonic Solutions for Systems of Differential Equations

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

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