Skip to main content

Two-point boundary value problems for higher-order linear differential equations with strong singularities

Abstract

For strongly singular higher-order linear differential equations together with two-point conjugate and right-focal boundary conditions, we provide easily verifiable best possible conditions which guarantee the existence of a unique solution.

[123456789101112131415161718]

References

  1. 1.

    Agarwal RP: Focal boundary value problems for differential and difference equations, Mathematics and Its Applications. Volume 436. Kluwer Academic Publishers, Dordrecht; 1998:x+289.

    Book  Google Scholar 

  2. 2.

    Agarwal RP, O'Regan D: Singular differential and integral equations with applications. Kluwer Academic Publishers, Dordrecht; 2003:xii+402.

    Book  MATH  Google Scholar 

  3. 3.

    Kiguradze IT: On a singular boundary value problem. Journal of Mathematical Analysis and Applications. 1970,30(3):475–489. 10.1016/0022-247X(70)90135-6

    MathSciNet  Article  MATH  Google Scholar 

  4. 4.

    Kiguradze IT: On a singular multi-point boundary value problem. Annali di Matematica Pura ed Applicata. Series IV. 1970, 86: 367–399. 10.1007/BF02415727

    MathSciNet  Article  MATH  Google Scholar 

  5. 5.

    Kiguradze I: Some singular boundary value problems for ordinary differential equations. Tbilisi University Press, Tbilisi; 1975.

    Google Scholar 

  6. 6.

    Kiguradze I: Some optimal conditions for the solvability of two-point singular boundary value problems. Functional Differential Equations 2003,10(1–2):259–281. Functional differential equations and applications (Beer-Sheva, 2002)

    MathSciNet  MATH  Google Scholar 

  7. 7.

    Kiguradze I: On two-point boundary value problems for higher order singular ordinary differential equations. Georgian Academy of Sciences. A. Razmadze Mathematical Institute. Memoirs on Differential Equations and Mathematical Physics 2004, 31: 101–107.

    MathSciNet  MATH  Google Scholar 

  8. 8.

    Kiguradze IT, Chanturia TA: Asymptotic properties of solutions of nonautonomous ordinary differential equations, Mathematics and Its Applications (Soviet Series). Volume 89. Kluwer Academic Publishers, Dordrecht; 1993:xiv+331. Translated from the 1985 Russian original

    Book  Google Scholar 

  9. 9.

    Kiguradze I, Půža B: Conti-Opial type existence and uniqueness theorems for nonlinear singular boundary value problems. Functional Differential Equations 2002,9(3–4):405–422. Dedicated to L. F. Rakhmatullina and N. V. Azbelev on the occasion of their seventieth and eightieth birthdays

    MathSciNet  MATH  Google Scholar 

  10. 10.

    Kiguradze I, Půža B, Stavroulakis IP: On singular boundary value problems for functional differential equations of higher order. Georgian Mathematical Journal 2001,8(4):791–814.

    MathSciNet  MATH  Google Scholar 

  11. 11.

    Kiguradze IT, Shekhter BL: Singular boundary value problems for second-order ordinary differential equations. In Current problems in mathematics. Newest results, Vol. 30 (Russian), Itogi Nauki i Tekhniki. Akad. Nauk SSSR Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., Moscow; 1987:105–201, 204. Translated in J. Soviet Math. 43 (1988), no. 2, 2340–2417

    Google Scholar 

  12. 12.

    Kiguradze I, Tskhovrebadze G: On two-point boundary value problems for systems of higher-order ordinary differential equations with singularities. Georgian Mathematical Journal 1994,1(1):31–45. 10.1007/BF02315301

    MathSciNet  Article  MATH  Google Scholar 

  13. 13.

    Maĭorov VE: On the existence of solutions of higher-order singular differential equations. Rossiĭskaya Akademiya Nauk. Matematicheskie Zametki 1992,51(3):75–84. translation in Math. Notes 51 (1992), no. 3–4, 274–281

    Google Scholar 

  14. 14.

    Půža B: On a singular two-point boundary value problem for the nonlinearth-order differential equation with deviating arguments. Georgian Mathematical Journal 1997,4(6):557–566. 10.1023/A:1022107625905

    MathSciNet  Article  MATH  Google Scholar 

  15. 15.

    Půža B, Rabbimov A: On a weighted boundary value problem for a system of singular functional-differential equations. Georgian Academy of Sciences. A. Razmadze Mathematical Institute. Memoirs on Differential Equations and Mathematical Physics 2000, 21: 125–130.

    MATH  Google Scholar 

  16. 16.

    Tskhovrebadze GD: On a multipoint boundary value problem for linear ordinary differential equations with singularities. Universitatis Masarykianae Brunensis. Facultas Scientiarum Naturalium. Archivum Mathematicum 1994,30(3):171–206.

    MathSciNet  MATH  Google Scholar 

  17. 17.

    Tskhovrebadze G: On the modified boundary value problem of de la Vallée–Poussin for nonlinear ordinary differential equations. Georgian Mathematical Journal 1994,1(4):429–458. 10.1007/BF02307450

    MathSciNet  Article  MATH  Google Scholar 

  18. 18.

    Wong PJY, Agarwal RP: Singular differential equations with boundary conditions. Mathematical and Computer Modelling 1998,28(1):37–44. 10.1016/S0895-7177(98)00079-X

    MathSciNet  Article  MATH  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to I Kiguradze.

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

Agarwal, R., Kiguradze, I. Two-point boundary value problems for higher-order linear differential equations with strong singularities. Bound Value Probl 2006, 83910 (2006). https://doi.org/10.1155/BVP/2006/83910

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1155/BVP/2006/83910

Keywords

  • Boundary Condition
  • Differential Equation
  • Partial Differential Equation
  • Unique Solution
  • Ordinary Differential Equation