Open Access

Second-order differential equations with deviating arguments

Boundary Value Problems20062006:23092

DOI: 10.1155/BVP/2006/23092

Received: 2 May 2006

Accepted: 28 May 2006

Published: 19 December 2006


This paper deals with boundary value problems for second-order differential equations with deviating arguments. Some sufficient conditions are formulated under which such problems have quasisolutions or a unique solution. A monotone iterative method is used. Examples with numerical results are added to illustrate the results obtained.


Authors’ Affiliations

Department of Differential Equations, Gdansk University of Technology


  1. Ding W, Han M, Mi J: Periodic boundary value problem for the second-order impulsive functional differential equations. Computers & Mathematics with Applications 2005,50(3-4):491-507. 10.1016/j.camwa.2005.03.010MathSciNetView ArticleMATHGoogle Scholar
  2. Jankowski T: Advanced differential equations with nonlinear boundary conditions. Journal of Mathematical Analysis and Applications 2005,304(2):490-503. 10.1016/j.jmaa.2004.09.059MathSciNetView ArticleMATHGoogle Scholar
  3. Jankowski T: On delay differential equations with nonlinear boundary conditions. Boundary Value Problems 2005,2005(2):201-214. 10.1155/BVP.2005.201MathSciNetView ArticleMATHGoogle Scholar
  4. Jankowski T: Solvability of three point boundary value problems for second order differential equations with deviating arguments. Journal of Mathematical Analysis and Applications 2005,312(2):620-636. 10.1016/j.jmaa.2005.03.076MathSciNetView ArticleMATHGoogle Scholar
  5. Jankowski T: Boundary value problems for first order differential equations of mixed type. Nonlinear Analysis 2006,64(9):1984-1997. 10.1016/ ArticleMATHGoogle Scholar
  6. Jiang D, Fan M, Wan A: A monotone method for constructing extremal solutions to second-order periodic boundary value problems. Journal of Computational and Applied Mathematics 2001,136(1-2):189-197. 10.1016/S0377-0427(00)00610-5MathSciNetView ArticleMATHGoogle Scholar
  7. Jiang D, Wei J: Monotone method for first- and second-order periodic boundary value problems and periodic solutions of functional differential equations. Nonlinear Analysis 2002,50(7):885-898. 10.1016/S0362-546X(01)00782-9MathSciNetView ArticleMATHGoogle Scholar
  8. Jiang D, Weng P, Li X: Periodic boundary value problems for second order differential equations with delay and monotone iterative methods. Dynamics of Continuous, Discrete & Impulsive Systems. Series A 2003,10(4):515-523.MathSciNetMATHGoogle Scholar
  9. Kolmanovskii V, Myshkis A: Introduction to the Theory and Applications of Functional Differential Equations, Mathematics and Its Applications. Volume 463. Kluwer Academic, Dordrecht; 1999:xvi+648.View ArticleMATHGoogle Scholar
  10. Ladde GS, Lakshmikantham V, Vatsala AS: Monotone Iterative Techniques for Nonlinear Differential Equations, Monographs, Advanced Texts and Surveys in Pure and Applied Mathematics. Volume 27. Pitman, Massachusetts; 1985:x+236.Google Scholar
  11. Nieto JJ, Rodríguez-López R: Existence and approximation of solutions for nonlinear functional differential equations with periodic boundary value conditions. Computers & Mathematics with Applications 2000,40(4-5):433-442. 10.1016/S0898-1221(00)00171-1MathSciNetView ArticleMATHGoogle Scholar
  12. Nieto JJ, Rodríguez-López R: Remarks on periodic boundary value problems for functional differential equations. Journal of Computational and Applied Mathematics 2003,158(2):339-353. 10.1016/S0377-0427(03)00452-7MathSciNetView ArticleMATHGoogle Scholar


© Jankowski and Szatanik 2006

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.