scholarly journals Monotone-Iterative Techniques of Lakshmikantham for a Boundary Value Problem for Systems of Differential Equations with Maxima

1995 ◽  
Vol 190 (2) ◽  
pp. 391-401 ◽  
Author(s):  
D.D. Bainov ◽  
S.G. Hristova
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Iterative Techniques ◽  
Monotone Iterative ◽  
Systems Of Differential Equations

scholarly journals A monotone iterative method for boundary value problems of parametric differential equations

2001 ◽  
Vol 14 (2) ◽  
pp. 183-187 ◽  
Author(s):  
Xinzhi Liu ◽  
Farzana A. McRae
Keyword(s):  
Differential Equations ◽  
Iterative Method ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Upper And Lower Solutions ◽  
Extremal Solutions ◽  
Monotone Iterative Method ◽  
Monotone Iterative ◽  
Monotone Sequences

This paper studies boundary value problems for parametric differential equations. By using the method of upper and lower solutions, monotone sequences are constructed and proved to converge to the extremal solutions of the boundary value problem.

scholarly journals An Integral Boundary Value Problem of Fractional Differential Equations with a Sign-Changed Parameter in Banach Spaces

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Chen Yang ◽  
Yaru Guo ◽  
Chengbo Zhai
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Banach Spaces ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Uniqueness Of Solutions ◽  
Integral Boundary ◽  
Integral Boundary Value Problem ◽  
Monotone Iterative ◽  
Fractional Differential

This paper is to investigate the existence and uniqueness of solutions for an integral boundary value problem of new fractional differential equations with a sign-changed parameter in Banach spaces. The main used approach is a recent fixed point theorem of increasing Ψ − h , r -concave operators defined on ordered sets. In addition, we can present a monotone iterative scheme to approximate the unique solution. In the end, two simple examples are given to illustrate our main results.

scholarly journals On the boundary value problem with integral conditions for the systems of differential equations of second order

1967 ◽  
Vol 7 (1) ◽  
pp. 59-77
Author(s):  
B. Kvedaras
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Second Order ◽  
Integral Conditions ◽  
Systems Of Differential Equations

The abstracts (in two languages) can be found in the pdf file of the article. Original author name(s) and title in Russian and Lithuanian: Б. Кведарас. О краевой задаче с интегральными условиями обыкновенных дифференциальных уравнений B. Kvedaras. Apie kraštinį uždavinį su integralinėmis sąlygomis antros eilės diferencialinių lygčių sistemoms

scholarly journals Monotone Iterative Technique and Ulam-Hyers Stability Analysis for Nonlinear Fractional Order Differential Equations with Integral Boundary Value Conditions

2019 ◽  
Vol 12 (2) ◽  
pp. 432-447
Author(s):  
Sajjad Ali ◽  
Kamal Shah ◽  
Hassan Khan ◽  
Muhammad Arif ◽  
Shahid Mahmood
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Fractional Differential Equations ◽  
Iterative Scheme ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Extremal Solutions ◽  
Integral Boundary ◽  
Monotone Iterative ◽  
Fractional Differential

In this manuscript, the monotone iterative scheme has been extended to the nature of solution to boundary value problem of fractional differential equation that consist integral boundary conditions. In this concern, some sufficient conditions are developed in this manuscript. On the base of sufficient conditions, the monotone iterative scheme combined with lower and upper solution method for the existence, uniqueness, error estimates and various view plots of the extremal solutions to boundary value problem of nonlinear fractional differential equations have been studied. The obtain results have clarified the nature of the extremal solutions. Further, the Ulam--Hyers and Ulam--Hyers--Rassias stability have been investigated for the considered problem.  Two illustrative examples of the BVP of the nonlinear fractional differential equations have been provided to justify our contribution.

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