Skip to main content
SpringerLink
Log in

On Compactness of Resolvent of a First Order Singular Differential Operator in Bounded Vector-Valued Function Space

  • Conference paper
  • First Online:
Functional Analysis in Interdisciplinary Applications (FAIA 2017)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 216))

Included in the following conference series:

  • 693 Accesses

Abstract

In this paper we give sufficient conditions for complete continuity of resolvent of a differential operator corresponding to a system of first order singular differential equations . Using coercive estimates for the solution of the above differential equation, we obtain the main result.

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

Access this chapter

Log in via an institution

Institutional subscriptions

References

  1. Dzhumabaev, D.S.: Method of parametrization for the decision of boundary value problems for ordinary differential equations. Vestnik AN KazSSR 1, 48–52 (1988)

    MATH  Google Scholar 

  2. Dzhumabaev, D.S.: Approximation of a bounded solution of the ordinary differential equation by solutions of the two-point boundary value problems. Comput. Math. Math. Phys. 30, 388–404 (1990)

    MathSciNet  MATH  Google Scholar 

  3. Kantorovich, L.V., Akilov, G.P.: Functional Analysis. Pergamon Press, Oxford (1982)

    MATH  Google Scholar 

  4. Martynov, V.V.: Conditions of discreteness and continuousness of the spectra in the case of self-adjoint system of differential equations. DAN SSSR 165, 996–999 (1965)

    Google Scholar 

  5. Mynbaev, K.T., Otelbaev, M.: Weighted Function Spaces and the Spectrum of Differential Operators. Nauka, Moscow (1988) (in Russian)

    Google Scholar 

  6. Oinarov, R., Otelbaev, M.: Discreteness criterion for the spectrum of the total of the general Sturm-Liouville operator and the associated embedding theorems. Differ. Equ. 24(2), 402–408 (1988)

    Google Scholar 

  7. Ospanov, K.N.: Qualitative and approximate characteristics of solutions of Beltrami-type systems. Complex Var. Elliptic Equ. 60, 1005–1014 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  8. Ospanov, K.N., Akhmetkaliyeva, R.D.: Some inequalities for second order differential operator with unbounded drift. Eurasian Math. J. 6, 63–74 (2015)

    MathSciNet  Google Scholar 

  9. Ospanov, M.N.: Coercive estimates for solutions of one singular equation with the third-order partial derivative. AIP Conf. Proc. 1611, 37–42 (2014)

    Article  Google Scholar 

  10. Ospanov, M.N.: The maximal regularity of the hyperbolic system. AIP Conf. Proc. 1676, 020037 (2015)

    Article  Google Scholar 

Download references

Acknowledgements

This work is partially supported by project 5132/GF4 of the Science Committee of Ministry of Education and Science of the Republic of Kazakhstan and by L.N. Gumilyov Eurasian National University Research Fund. This publication is supported by the target program 0085/PTSF-14 from the Ministry of Science and Education of the Republic of Kazakhstan.

Author information

Authors and Affiliations

  1. L.N. Gumilyov Eurasian National University, 2 Satpaev st., Astana, 010008, Kazakhstan

    Myrzagali N. Ospanov

Authors
  1. Myrzagali N. Ospanov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Myrzagali N. Ospanov .

Editor information

Editors and Affiliations

  1. Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan

    Tynysbek Sh. Kalmenov

  2. Department of Mechanics and Mathematics, Kazakhstan Branch of Lomonosov Moscow State University, Astana, Kazakhstan

    Erlan D. Nursultanov

  3. Department of Mathematics, Imperial College London, London, United Kingdom

    Michael V. Ruzhansky

  4. Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan

    Makhmud A. Sadybekov

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Ospanov, M.N. (2017). On Compactness of Resolvent of a First Order Singular Differential Operator in Bounded Vector-Valued Function Space. In: Kalmenov, T., Nursultanov, E., Ruzhansky, M., Sadybekov, M. (eds) Functional Analysis in Interdisciplinary Applications. FAIA 2017. Springer Proceedings in Mathematics & Statistics, vol 216. Springer, Cham. https://doi.org/10.1007/978-3-319-67053-9_28

Download citation

Publish with us

Policies and ethics

Search

Navigation