## Abstract and Applied Analysis

### Monotone-Iterative Method for Solving Antiperiodic Nonlinear Boundary Value Problems for Generalized Delay Difference Equations with Maxima

#### Abstract

A nonlinear generalized difference equation with both delays and the maximum value of the unknown function over a discrete past time interval are studied. A nonlinear boundary value problem of antiperiodic type for the given difference equation is set up. One of the main characteristics of the considered difference equation is the presence of the unknown function in both sides of the equation. It leads to impossibility for using the step method for explicit solving of the nonlinear difference equation. In this paper, an approximate method, namely, the monotone iterative technique, is applied to solve the problem. An important feature of the given algorithm is that each successive approximation of the unknown solution is equal to the unique solution of an appropriately constructed initial value problem for a linear difference equation with “maxima,” and an algorithm for its explicit solving is given. Also, each approximation is a lower/upper solution of the given nonlinear boundary value problem. The suggested scheme for approximate solving is computer realized, and it is applied to a particular example, which is a generalization of a model in population dynamics.

#### Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 571954, 9 pages.

Dates
First available in Project Euclid: 27 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393512014

Digital Object Identifier
doi:10.1155/2013/571954

Mathematical Reviews number (MathSciNet)
MR3093766

Zentralblatt MATH identifier
1291.39001

#### Citation

Golev, Angel; Hristova, Snezhana; Nenov, Svetoslav. Monotone-Iterative Method for Solving Antiperiodic Nonlinear Boundary Value Problems for Generalized Delay Difference Equations with Maxima. Abstr. Appl. Anal. 2013 (2013), Article ID 571954, 9 pages. doi:10.1155/2013/571954. https://projecteuclid.org/euclid.aaa/1393512014

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