Theory and applications of first-order systems of Stieltjes differential equations

2017 ◽  
Vol 6 (1) ◽  
pp. 13-36 ◽  
Author(s):  
Marlène Frigon ◽  
Rodrigo López Pouso
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Time Scales ◽  
Existence And Uniqueness ◽  
Basic Theory ◽  
Dynamic Equations ◽  
Uniqueness Of Solutions ◽  
First Order ◽  
Systems Of Differential Equations ◽  
Set Up

AbstractWe set up the basic theory of existence and uniqueness of solutions for systems of differential equations with usual derivatives replaced by Stieltjes derivatives. This type of equations contains as particular cases dynamic equations on time scales and impulsive ordinary differential equations.

scholarly journals Convergence of Antiperiodic Boundary Value Problems for First-Order Integro-Differential Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Yameng Wang ◽  
Juan Zhang ◽  
Yufeng Sun
Keyword(s):  
Differential Equations ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Approximate Solutions ◽  
Lower And Upper Solutions ◽  
Quasilinearization Method ◽  
Rapid Convergence ◽  
Uniqueness Of Solutions ◽  
First Order ◽  
Convergence Of Approximate Solutions

In this paper, we investigate the convergence of approximate solutions for a class of first-order integro-differential equations with antiperiodic boundary value conditions. By introducing the definitions of the coupled lower and upper solutions which are different from the former ones and establishing some new comparison principles, the results of the existence and uniqueness of solutions of the problem are given. Finally, we obtain the uniform and rapid convergence of the iterative sequences of approximate solutions via the coupled lower and upper solutions and quasilinearization method. In addition, an example is given to illustrate the feasibility of the method.

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