Skip to main content
Boundary Value Problems
Download PDF

Second-order differential equations with deviating arguments

Boundary Value Problems volume 2006, Article number: 23092 (2006) Cite this article

Abstract

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.

[123456789101112]

References

  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.2005.03.010

    MathSciNet  Article  MATH  Google 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.2004.09.059

    MathSciNet  Article  MATH  Google Scholar 

  3. Jankowski T: On delay differential equations with nonlinear boundary conditions. Boundary Value Problems 2005,2005(2):201-214. 10.1155/BVP.2005.201

    MathSciNet  Article  MATH  Google 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.2005.03.076

    MathSciNet  Article  MATH  Google Scholar 

  5. Jankowski T: Boundary value problems for first order differential equations of mixed type. Nonlinear Analysis 2006,64(9):1984-1997. 10.1016/j.na.2005.07.033

    MathSciNet  Article  MATH  Google 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)00610-5

    MathSciNet  Article  MATH  Google 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)00782-9

    MathSciNet  Article  MATH  Google 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.

    MathSciNet  MATH  Google 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.

    Book  MATH  Google 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)00171-1

    MathSciNet  Article  MATH  Google 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)00452-7

    MathSciNet  Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Differential Equations, Gdansk University of Technology, 11/12 G. Narutowicz Street, Gdańsk, 80-952, Poland

    T Jankowski & W Szatanik

Authors
  1. T Jankowski
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. W Szatanik
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to T Jankowski.

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Reprints and Permissions

About this article

Cite this article

Jankowski, T., Szatanik, W. Second-order differential equations with deviating arguments. Bound Value Probl 2006, 23092 (2006). https://doi.org/10.1155/BVP/2006/23092

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1155/BVP/2006/23092

Keywords

  • Differential Equation
  • Partial Differential Equation
  • Unique Solution
  • Ordinary Differential Equation
  • Functional Equation