Monotone iterative method for first-order differential equations at resonance

2014 ◽  
Vol 233 ◽  
pp. 20-28 ◽  
Author(s):  
Tadeusz Jankowski
Keyword(s):  
Differential Equations ◽  
Iterative Method ◽  
Monotone Iterative Method ◽  
First Order ◽  
Monotone Iterative ◽  
At Resonance ◽  
First Order Differential Equations

Monotone Iterative Techniques and a Periodic Boundary Value Problem for First Order Differential Equations with a Functional Argument

2000 ◽  
Vol 7 (2) ◽  
pp. 373-378
Author(s):  
Aiqin Qi ◽  
Yansheng Liu
Keyword(s):  
Differential Equations ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Upper And Lower Solutions ◽  
Initial Value ◽  
First Order ◽  
Monotone Iterative ◽  
Periodic Boundary Value Problems ◽  
Functional Argument ◽  
First Order Differential Equations

Abstract This paper is concerned with periodic boundary value problems involving first order differential equations with functional arguments. The main feature of the paper is that the existence of maximal and minimal solutions is obtained by constructing sequences of upper and lower solutions of the initial value problems and not by establishing the comparison principle.

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.

Monotone iterative method for a class of nonlinear fractional differential equations

2012 ◽  
Vol 15 (2) ◽  
Author(s):  
Guotao Wang ◽  
Dumitru Baleanu ◽  
Lihong Zhang
Keyword(s):  
Differential Equations ◽  
Iterative Method ◽  
Fractional Differential Equations ◽  
Monotone Iterative Technique ◽  
Monotone Iterative Method ◽  
Iterative Technique ◽  
Nonlinear Fractional Differential Equations ◽  
Monotone Iterative ◽  
Liouville Fractional Derivative ◽  
Fractional Differential

AbstractBy applying the monotone iterative technique and the method of lower and upper solutions, this paper investigates the existence of extremal solutions for a class of nonlinear fractional differential equations, which involve the Riemann-Liouville fractional derivative D q x(t). A new comparison theorem is also build. At last, an example is given to illustrate our main results.

scholarly journals Oscillation in deviating differential equations using an iterative method

2019 ◽  
Vol 27 (2) ◽  
pp. 143-169 ◽  
Author(s):  
George E. Chatzarakis ◽  
Irena Jadlovská
Keyword(s):  
Differential Equations ◽  
Iterative Method ◽  
Gronwall Inequality ◽  
Deviating Arguments ◽  
First Order ◽  
Grönwall Inequality ◽  
Nonnegative Coefficients ◽  
First Order Differential Equations

AbstractSufficient oscillation conditions involving lim sup and lim inf for first-order differential equations with non-monotone deviating arguments and nonnegative coefficients are obtained. The results are based on the iterative application of the Grönwall inequality. Examples, numerically solved in MATLAB, are also given to illustrate the applicability and strength of the obtained conditions over known ones.

scholarly journals Monotone iterative method for fractional p-Laplacian differential equations with four-point boundary conditions

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Xiaoping Li ◽  
Minyuan He
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Iterative Method ◽  
Boundary Conditions ◽  
Boundary Problem ◽  
Positive Solutions ◽  
Monotone Iterative Method ◽  
Point Boundary ◽  
Abstract Result ◽  
Monotone Iterative

AbstractA four-point boundary problem for a fractional p-Laplacian differential equation is studied. The existence of two positive solutions is established by means of the monotone iterative method. An example supporting the abstract result is given.

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