Skip to main content

Existence and Uniqueness of a Positive Solution to a Boundary Value Problem for a Second Order Functional-Differential Equation

Russian Mathematics volume 65, pages 1–5 (2021)Cite this article

Abstract

In the paper, we consider a boundary value problem for a second order functional-differential equation with sufficiently general linear homogeneous boundary conditions. On the basis of the theory of semi-ordered spaces and with the help of special topological methods, we prove the existence of a unique positive solution to the problem.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

USD 39.95

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

REFERENCES

  1. Azbelev N.V., Maksimov V.P., Simonov P.M. "Functional differential equations and their applications", Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, Ser. Matem. 1, 3-23 (2009) [in Russian].

    Google Scholar 

  2. Wong F.H., Wang S.P., Chen T.G. "Existence of positive solutions for second order functional differential equations", Comput. and Math. Appl. 56 (10), 2580-2587 (2008).

    MathSciNet  Article  Google Scholar 

  3. Ma R. "Positive solutions for boundary value problems of functional differential equations", Appl. Math. Comput. 193 (1), 66-72 (2007).

    MathSciNet  MATH  Google Scholar 

  4. Zima M. "On positive solutions of functional-differential equations in banach spaces", J. Inequalities and Appl. 6 (3), 359-371 (2000).

    MathSciNet  MATH  Google Scholar 

  5. Agarwal R.P., Stanek S. "Positive solutions of singular value problems for delay differential equations", Dyn. Syst. Appl. 16 (4), 755-770 (2007).

    MathSciNet  MATH  Google Scholar 

  6. Hong C., Yeh C., Lee C., Wong F. "Existence of positive solutions for functional equations", Comp. Math. Appl. 40 (6–7), 783-792 (2000).

    MathSciNet  Article  Google Scholar 

  7. Sun Y., Han M.M., Debnath L. "Existence of positive periodic solutions for a class of functional differential equations", Appl. Math. Comput. 190 (1), 699-704 (2007).

    MathSciNet  MATH  Google Scholar 

  8. Weng P., Jiang D. "Existence of positive solutions for boundary value problem of second-order FDE", Comput. Math. Appl. 37 (10), 1-9 (1999).

    MathSciNet  Article  Google Scholar 

  9. Hong C., Yeh C., Lee C., Wong F. "Existence of positive solutions for higher-order functional differential equations", J. Math. Anal. Appl. 297 (1), 14-23 (2004).

    MathSciNet  Article  Google Scholar 

  10. Yin F., Fugi F., Li Y. "The existence of positive solutions for the quasilinear functional delay differential equations", J. Math. Study 35 (4), 364-370 (2002).

    MathSciNet  Google Scholar 

  11. Krasnosel'skii M.A. Positive Solutions of Operator Equations (Fizmatgiz, Moscow, 1962) [in Russian].

    MATH  Google Scholar 

  12. Abduragimov G.E. "On positive solutions of boundary value problem for a nonlinear functional-differential equation of the 2nd order", Vestn. Dagest. Gos. Univ. Estestv. Nauki IV, 121-123 (1997) [in Russian].

    Google Scholar 

  13. Krein S.G. Functional Analysis (Nauka, Moscow, 1972) [in Russian].

    Google Scholar 

  14. Zabreiko P.P., Krasnosel'skii P.P., Stetsenko V.Ya. "Estimates of the spectral radius of positive linear operators", Math. Notes 1 (4), 306-310 (1967).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dagestan State University, 12 Dzerzhinsky str., 367000, Makhachkala, Russia

    G. E. Abduragimov

Authors
  1. G. E. Abduragimov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to G. E. Abduragimov.

Additional information

Dedicated to the bright memory of my father, Abduragimov Elderkhan Israpilovich

Russian Text © The Author(s), 2021, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2021, No. 12, pp. 3–8.

About this article

Verify currency and authenticity via CrossMark

Cite this article

Abduragimov, G.E. Existence and Uniqueness of a Positive Solution to a Boundary Value Problem for a Second Order Functional-Differential Equation. Russ Math. 65, 1–5 (2021). https://doi.org/10.3103/S1066369X2112001X

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S1066369X2112001X

Keywords

  • positive solution
  • boundary value problem
  • cone
  • asymptotic derivative
  • spectral radius.