Averaging of a boundary-value problem for a multifrequency system with deviating argument

2007 ◽  
Vol 10 (4) ◽  
pp. 0-0
Author(s):  
R. I. Petryshyn ◽  
I. M. Danylyuk
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Deviating Argument ◽  
Multifrequency System

Numerical methods for solving the first-kind boundary value problem for a linear second-order differential equation with a deviating argument

2017 ◽  
Vol 23 (2) ◽  
Author(s):  
Muhad H. Abregov ◽  
Vladimir Z. Kanchukoev ◽  
Maryana A. Shardanova
Keyword(s):  
Differential Equation ◽  
Numerical Methods ◽  
Finite Difference ◽  
Boundary Value Problem ◽  
Order Differential Equation ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Second Order ◽  
Deviating Argument ◽  
Second Order Differential Equation

AbstractThis work is devoted to the numerical methods for solving the first-kind boundary value problem for a linear second-order differential equation with a deviating argument in minor terms. The sufficient conditions of the one-valued solvability are established, and the a priori estimate of the solution is obtained. For the numerical solution, the problem studied is reduced to the equivalent boundary value problem for an ordinary linear differential equation of fourth order, for which the finite-difference scheme of second-order approximation was built. The convergence of this scheme to the exact solution is shown under certain conditions of the solvability of the initial problem. To solve the finite-difference problem, the method of five-point marching of schemes is used.

scholarly journals Multiple Positive Solutions for a Fractional Boundary Value Problem with Fractional Integral Deviating Argument

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
A. Guezane-Lakoud ◽  
R. Khaldi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Point Theorem ◽  
Fractional Integral ◽  
Boundary Value ◽  
Multiple Positive Solutions ◽  
Fractional Boundary Value Problem ◽  
Deviating Argument

This work is devoted to the existence of positive solutions for a fractional boundary value problem with fractional integral deviating argument. The proofs of the main results are based on Guo-Krasnoselskii fixed point theorem and Avery and Peterson fixed point theorem. Two examples are given to illustrate the obtained results, ending the paper.

scholarly journals A fixed-point approach for decaying solutions of difference equations

2021 ◽  
Vol 379 (2191) ◽  
pp. 20190374
Author(s):  
Zuzana Došlá ◽  
Mauro Marini ◽  
Serena Matucci
Keyword(s):  
Fixed Point ◽  
Difference Equation ◽  
Boundary Value Problem ◽  
Difference Equations ◽  
Boundary Value ◽  
Future Research ◽  
Deviating Argument ◽  
Advanced Argument ◽  
Intermediate Solution ◽  
The Difference

A boundary value problem associated with the difference equation with advanced argument * Δ ( a n Φ ( Δ x n ) ) + b n Φ ( x n + p ) = 0 , n ≥ 1 is presented, where Φ ( u ) = | u | α sgn u , α  > 0, p is a positive integer and the sequences a , b , are positive. We deal with a particular type of decaying solution of (*), that is the so-called intermediate solution (see below for the definition). In particular, we prove the existence of this type of solution for (*) by reducing it to a suitable boundary value problem associated with a difference equation without deviating argument. Our approach is based on a fixed-point result for difference equations, which originates from existing ones stated in the continuous case. Some examples and suggestions for future research complete the paper. This article is part of the theme issue ‘Topological degree and fixed point theories in differential and difference equations’.

Sign in / Sign up

Export Citation Format

Share Document