Block Monotone Iterative Method for Semilinear Parabolic Equations with Nonlinear Boundary Conditions

2010 ◽  
Vol 47 (6) ◽  
pp. 4581-4606 ◽  
Author(s):  
C. V. Pao ◽  
Xin Lu
Keyword(s):  
Iterative Method ◽  
Boundary Conditions ◽  
Parabolic Equations ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Conditions ◽  
Monotone Iterative Method ◽  
Semilinear Parabolic Equations ◽  
Monotone Iterative ◽  
Semilinear Parabolic

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.

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.

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