scholarly journals Monotone iterative method for differential systems with coupled integral boundary value problems

2013 ◽  
Vol 2013 (1) ◽  
Author(s):  
Yujun Cui ◽  
Yumei Zou
Keyword(s):  
Iterative Method ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Monotone Iterative Method ◽  
Integral Boundary ◽  
Differential Systems ◽  
Monotone Iterative ◽  
Integral Boundary Value Problems

scholarly journals Monotone Iterative Method for Two Types of Integral Boundary Value Problems of a Nonlinear Fractional Differential System with Deviating Arguments

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Jungang Chen ◽  
Xi Qin
Keyword(s):  
Iterative Method ◽  
Boundary Value Problems ◽  
Differential System ◽  
Boundary Value ◽  
Monotone Iterative Method ◽  
Integral Boundary ◽  
Monotone Iterative ◽  
Fractional Differential System ◽  
Fractional Differential ◽  
Integral Boundary Value Problems

This paper concerns on two types of integral boundary value problems of a nonlinear fractional differential system, i . e ., nonlocal strip integral boundary value problems and coupled integral boundary value problems. With the aid of the monotone iterative method combined with the upper and lower solutions, the existence of extremal system of solutions for the above two types of differential systems is investigated. In addition, a new comparison theorem for fractional differential system is also established, which is crucial for the proof of the main theorem of this paper. At the end, an example explaining how our studies can be used is also given.

The monotone iterative method for the integral boundary value problems of fractional p-Laplacian equations with delay

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Chunyan Wei ◽  
Xiping Liu ◽  
Mei Jia ◽  
Luchao Zhang
Keyword(s):  
Iterative Method ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Monotone Iterative Method ◽  
Integral Boundary ◽  
Monotone Iterative ◽  
Liouville Derivative ◽  
Integral Boundary Value Problems ◽  
Laplacian Equations ◽  
Equations With Delay

AbstractBased on the theory of lower and upper solutions, we study the monotone iterative method for the nonlinear integral boundary value problems of fractional p-Laplacian equations with delay, which involves both Riemann–Liouville derivative and Caputo derivative. Some new results on the existence of positive solutions are established and the iterative methods for finding approximate solutions of the boundary value problem are obtained. Finally, two examples are given out to illustrate the numerical solution and the related graphic simulations are also provided.

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 Multiplicity Results for Positive Solutions to Differential Systems of Singular Coupled Integral Boundary Value Problems

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Yujun Cui
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problems ◽  
Multiple Solutions ◽  
Boundary Value ◽  
Integral Boundary ◽  
Differential Systems ◽  
Multiplicity Results ◽  
Integral Boundary Value Problems ◽  
Special Cone

By constructing a special cone and using a fixed-point theorem in cone, this paper investigates the existence of multiple solutions of coupled integral boundary value problems for a nonlinear singular differential system.

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