Skip to main content
Log in

Boundary value problems for differential equations with deviating arguments

  • Research Papers
  • Published:
aequationes mathematicae Aims and scope Submit manuscript

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.

References

  1. Aliev, R. M.,On a Boundary Value Problem for Second Order Linear Differential Equations with Retarded Argument (Russian), inProc. Second Scientific Conference at Moscow's People's Friendship University (1966), pp. 15–16.

  2. Driver, R. D.,Existence and Stability of Solutions of a Delay-Differential System, Arch. Rational Mech. Anal.10, 401–426 (1962).

    Google Scholar 

  3. —,Existence Theory for a Delay-Differential System, Contrib. Diff. Equations1, 317–336 (1963).

    Google Scholar 

  4. —,Existence and Continuous Dependence of Solutions of a Neutral Functional-Differential Equation, Arch. Rational Mech. Anal.19, 149–166 (1965).

    Google Scholar 

  5. Dunford N. andSchwartz, J.,Linear Operators, Part I:General Theory (Interscience, New York 1958).

    Google Scholar 

  6. El'sgol'ts, L. E.,Introduction to the Theory of Differential Equations with Deviating Arguments (Holden-Day, San Francisco 1966).

    Google Scholar 

  7. Grimm, L. J., andSchmitt, K.,Boundary Value Problems for Delay-Differential Equations, Bull. Amer. Math. Soc.74, 997–1000 (1968).

    Google Scholar 

  8. Hartman, P.,Ordinary Differential Equations (Wiley, New York 1964).

    Google Scholar 

  9. Jackson, L. K. andSchrader, K.,Comparison Theorems for Nonlinear Differential Equations, J. Differential Equations3, 248–255 (1967).

    Google Scholar 

  10. Jackson, L. K.,Subfunctions and Boundary Value Problems for Second Order Ordinary Differential Equations, Advances in Math.2, 307–363 (1968).

    Google Scholar 

  11. G. A. Kamenskii,Boundary Value Problems for Nonlinear Equations with Perturbed Arguments (Russian), Nauk-Dokl. Vyssh. Shkoly Fiz. Mat. Nauki2, 60–66 (1958).

    Google Scholar 

  12. —,Boundary Value Problems for Nonlinear Differential Equations with Deviating Arguments of Neutral Type (Russian), Trudy Sem. Teor. Diff. Urav. Otklon. Arg.1, 47–51 (1962).

    Google Scholar 

  13. —,On Uniqueness of Solutions of Boundary Value Problems for Nonlinear Second Order Differential Equations with Deviating Arguments of Neutral Type (Russian),ibid. 4, 274–277 (1967).

    Google Scholar 

  14. —, andEl'sgol'ts, L. E.,Some Directions of Investigation on the Theory of Differential Equations with Deviating Argument (Russian),ibid. 6, 3–36 (1968).

    Google Scholar 

  15. Knobloch, H. W.,Eine neue Methode zur Approximation periodischer Lösungen nicht-linearer Differentialgleichungen zweiter Ordnung, Math. Z.82, 177–197 (1962).

    Google Scholar 

  16. Martynjuk, D. I.,Periodic Solutions of Nonlinear Second Order Differential Equations with Retarded Arguments (Russian), Ukrain. Mat. Žh.19, 125–132 (1967).

    Google Scholar 

  17. Mikolajska, Z.,Une remarque sur l'existence d'une solution périodique d'une équation différo-différentielle aux deuxième membre croissant, Ann. Polon. Mat.18, 53–58 (1966).

    Google Scholar 

  18. Myshkis, A. D., andEl'sgol'ts, L. E.,Some Results and Problems in the Theory of Differential Equations, Uspehi Mat. Nauk,22, 21–57 (1967) = Russian Math. Surveys22, 19–57 (1967).

    Google Scholar 

  19. Norkin, S. B.,On a Boundary Value Problem for a Second Order Differential Equation with a Retarded Argument on a Half-Axis (Russian), Trudy Sem. Diff. Urav. Otklon. Arg.2, 162–171 (1963).

    Google Scholar 

  20. —,Second Order Differential Equations with Retarded Argument (Russian) (Nauka, Moscow 1965).

    Google Scholar 

  21. Schmitt, K.,Periodic Solutions of Nonlinear Second Order Differential Equations, Math. Z.98, 200–207 (1967).

    Google Scholar 

  22. —,Boundary Value Problems for Nonlinear Second Order Differential Equations, Monatsh. Math.72, 374–354 (1968).

    Google Scholar 

  23. —,Bounded Solutions of Nonlinear Second Order Differential Equations, Duke Math. J.36, 2 (1969).

    Google Scholar 

  24. Schrader, K. W.,Boundary Value Problems for Second-Order Ordinary Differential Equations. J. Differential Equations3, 403–413 (1967).

    Google Scholar 

  25. Zverkin, A. M., Kamenskii, G. A., Norkin, S. B., andEl'sgol'ts, L. E.,Differential Equations with a Perturbed Argument, Uspehi Mat. Nauk. 17, 77–164 (1962) = Russian Math. Surveys17, 61–146 (1962).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Grimm, L.J., Schmitt, K. Boundary value problems for differential equations with deviating arguments. Aeq. Math. 4, 176–190 (1970). https://doi.org/10.1007/BF01817758

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01817758

Keywords

Navigation