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Second-order differential equations with deviating arguments

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.

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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 

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Correspondence to T Jankowski.

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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.

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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

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

Keywords

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