Ordinary Differential Equations with Nonlinear Boundary Conditions

2002 ◽  
Vol 9 (2) ◽  
pp. 287-294
Author(s):  
Tadeusz Jankowski
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Ordinary Differential Equations ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Conditions ◽  
Existence Results ◽  
Monotone Iterative Technique ◽  
Lower And Upper Solutions ◽  
Iterative Technique ◽  
Monotone Iterative

Abstract The method of lower and upper solutions combined with the monotone iterative technique is used for ordinary differential equations with nonlinear boundary conditions. Some existence results are formulated for such problems.

Nonconvex Differential Inclusions with Nonlinear Monotone Boundary Conditions

1997 ◽  
Vol 4 (6) ◽  
pp. 501-508
Author(s):  
S. A. Brykalov
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Differential Inclusions ◽  
Nonlinear Boundary ◽  
Functional Differential Equations ◽  
Nonlinear Boundary Conditions ◽  
Existence Results ◽  
Selection Theorem ◽  
Functional Differential ◽  
Nonconvex Differential Inclusions

Abstract Existence results for problems with monotone nonlinear boundary conditions obtained in the previous publications by the author for functional differential equations are transferred to the case of nonconvex differential inclusions with the help of the selection theorem due to A. Bressan and G. Colombo.

scholarly journals A generalized upper and lower solutions method for nonlinear second order ordinary differential equations

1992 ◽  
Vol 5 (2) ◽  
pp. 157-165 ◽  
Author(s):  
Juan J. Nieto ◽  
Alberto Cabada
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Nonlinear Boundary ◽  
Upper And Lower Solutions ◽  
Monotone Iterative Technique ◽  
Second Order ◽  
Iterative Technique ◽  
Monotone Iterative ◽  
Carathéodory Function ◽  
Minimal And Maximal Solutions

The purpose of this paper is to study a nonlinear boundary value problem of second order when the nonlinearity is a Carathéodory function. It is shown that a generalized upper and lower solutions method is valid, and the monotone iterative technique for finding the minimal and maximal solutions is developed.

scholarly journals Convergence of solutions for functional integro-differential equations with nonlinear boundary conditions

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Peiguang Wang ◽  
Yameng Wang ◽  
Cuimei Jiang ◽  
Tongxing Li
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Unique Solution ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Conditions ◽  
Quasilinearization Method ◽  
Comparison Principles ◽  
Monotone Iterative ◽  
Convergence Of Solutions

AbstractThis paper is concerned with the convergence of solutions for a class of functional integro-differential equations with nonlinear boundary conditions. New comparison principles are obtained. By using the comparison principles and quasilinearization method, we present two monotone iterative sequences uniformly and monotonically converging to the unique solution with rate of order 2. Meanwhile, an example is given to demonstrate applications of the result reported.

scholarly journals Monotone Iterative Method for ψ-Caputo Fractional Differential Equation with Nonlinear Boundary Conditions

2021 ◽  
Vol 5 (3) ◽  
pp. 81
Author(s):  
Zidane Baitiche ◽  
Choukri Derbazi ◽  
Jehad Alzabut ◽  
Mohammad Esmael Samei ◽  
Mohammed K. A. Kaabar ◽  
...  
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Fractional Differential Equation ◽  
Nonlinear Boundary ◽  
Upper And Lower Solutions ◽  
Nonlinear Boundary Conditions ◽  
Monotone Iterative Technique ◽  
Monotone Iterative Method ◽  
Monotone Iterative ◽  
Fractional Differential

The main contribution of this paper is to prove the existence of extremal solutions for a novel class of ψ-Caputo fractional differential equation with nonlinear boundary conditions. For this purpose, we utilize the well-known monotone iterative technique together with the method of upper and lower solutions. Finally, we provide an example along with graphical representations to confirm the validity of our main results.

Sign in / Sign up

Export Citation Format

Share Document