Skip to main content
Log in

Boundary Value Problems for Ordinary Differential Equations with Deviated Arguments

  • Published:
Journal of Optimization Theory and Applications Aims and scope Submit manuscript

Abstract

We discuss differential equations with nonlinear boundary conditions. We formulate sufficient conditions under which problems with deviating arguments have quasisolutions or solutions. To obtain the results, we apply the method of monotone iterations.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Jankowski, T.: On delay differential equations with nonlinear boundary conditions. Bound. Value Probl. 2005(2), 201–214 (2005)

    Article  MathSciNet  Google Scholar 

  2. Ladde, G.S., Lakshmikantham, V., Vatsala, A.S.: Monotone Iterative Techniques for Nonlinear Differential Equations. Pitman Advanced Publishing Program, Boston (1985)

    MATH  Google Scholar 

  3. Jankowski, T.: Existence of solutions of boundary value problems for differential equations with delayed arguments. J. Comput. Appl. Math. 156, 239–252 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  4. Jankowski, T.: Advanced differential equations with nonlinear boundary conditions. J. Math. Anal. Appl. 304, 490–503 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  5. Jiang, D., Wei, J.: Monotone method for first-and second-order periodic boundary value problems and periodic solutions of functional differential equations. Nonlinear Anal. 50, 885–898 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  6. Liz, E., Nieto, J.J.: Periodic boundary value problems for a class of functional differential equations. J. Math. Anal. Appl. 200, 680–686 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  7. Nieto, J.J., Rodríguez-López, R.: Existence and approximation of solutions for nonlinear functional differential equations with periodic boundary value conditions. Comput. Math. Appl. 40, 433–442 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  8. Nieto, J.J., Rodríguez-López, R.: Remarks on periodic boundary value problems for functional differential equations. J. Comput. Appl. Math. 158, 339–353 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  9. Jankowski, T.: Solvability of three point boundary value problems for second order differential equations with deviating arguments. J. Math. Anal. Appl. 312, 620–636 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  10. Jiang, D., Weng, P., Li, X.: Periodic boundary value problems for second order differential equations with delay and monotone iterative methods. Dyn. Contin. Discret. Impuls. Syst. Ser. A Math. Anal. 10A, 515–523 (2003)

    MathSciNet  Google Scholar 

  11. Ding, W., Han, M., Mi, J.: Periodic boundary value problem for second-order impulsive functional differential equations. Comput. Math. Appl. 50, 491–507 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  12. Ding, W., Mi, J., Han, M.: Periodic boundary value problems for the first order impulsive functional differential equations. Appl. Math. Comput. 165, 433–446 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  13. He, Z., Yu, J.: Periodic boundary value problem for first-order impulsive functional differential equations. J. Comput. Appl. Math. 138, 205–217 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  14. Zhang, F., Ma, Z., Yan, J.: Boundary value problems for first order impulsive delay differential equations with a parameter. J. Math. Anal. Appl. 290, 213–223 (2004)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to T. Jankowski.

Additional information

Communicated by F. Zirilli.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dyki, A., Jankowski, T. Boundary Value Problems for Ordinary Differential Equations with Deviated Arguments. J Optim Theory Appl 135, 257–269 (2007). https://doi.org/10.1007/s10957-007-9248-3

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10957-007-9248-3

Keywords

Navigation