Skip to main content
SpringerLink
Log in

Boundary value problems associated with multiple roots of the characteristic equation

  • Published:
Results in Mathematics Aims and scope Submit manuscript

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Literature

  1. W. Eberhard and G. Freiling, Stone - reguläre Eigenwertprobleme. Math. Z. 160, 139–161 (1978).

    Article  MathSciNet  MATH  Google Scholar 

  2. G. Frei Ling, Reguläre Eigenwertprobleme mit Mehrpunkt-Integral-Randbedingungen. Math. Z. 171, 113–131 (1980)

    MathSciNet  Google Scholar 

  3. M.G. Gasymov and A.M. Magerramov, Investigation of a class of differential operator pencils of even onder. Soviet Math Dokl. 26, 55–58 (1982).

    MATH  Google Scholar 

  4. G. Heisecke, Rand-Eigenwertprobleme N(y) = λP(y) bei λ-abhängigen Randbedingungen. Mitt. Math. Sem. Gießen 145, 1–74 (1980).

    MathSciNet  Google Scholar 

  5. R.E. Langer, On the zeros of exponential sums and integrals. Bull. Am. Math. Soc. 37, 213–239 (1931).

    Article  Google Scholar 

  6. R.E. Langer, The boundary problem of an ordinary linean. differential system in the complex domain. Trans. Am. Soc. 46, 151–190 (1939), correction 467.

    Google Scholar 

  7. L.A. McColl, On the distribution of the zeros of sums of exponentials and polynomials. Trans. Am. Math. Soc. 36, 341–360 (1934).

    Google Scholar 

  8. M.A. Naimark, Linear differential operators, port I and part II. F. Ungar, New York, 1967.

    Google Scholar 

  9. P. Noaillon, Développements asymptotiques dans les équations differentielles linéaires á paramétre variable. Mémoires de la Soc. des Sc. de Liège, 3. Série, IX, 197 pages (1912).

    Google Scholar 

  10. M.B. Orazov and A.A. Shkalikov, Then n-fold basis property of the characteristic functions of certain regular. boundary-value, problems. Sib. Math. J. 17, 483–492 (1976).

    Article  Google Scholar 

  11. A.S. Pechentsov, Asymptotic expansions of linear differential equations containing a porameter. Diff. Equ. 17, 1023–1031 (1981).

    MathSciNet  MATH  Google Scholar 

  12. A.S. Pechentsov, Roundary-value problems for. differential equations with. a panameter, having charcteristic equations with multiple roots. Diff. Equ. 20, 206–215 (1984).

    MathSciNet  MATH  Google Scholar 

  13. M.H. Stone, A comparison of the series of Fourier and Birkhoff. Trans. Am. Math. Soc. 28, 695–761 (1926).

    Article  Google Scholar 

  14. J.D. Tamarkin, Some general problems of the theory of ordinary linear differential equations and. expansions of an arbitrary function in series of fundamental functions. Math. Z. 27, 1–54 (1927).

    Article  MathSciNet  MATH  Google Scholar 

  15. W.J. Trjitzinsky, Theory of linear differential equations containing a parameter. Acta Math. 67, 1–50 (1936).

    Article  MathSciNet  Google Scholar 

  16. H.L. Turrittin, Asymptotic solutions of certain ordinary differential equations associated with multiple roots of the characteristic equation. Am. J. of Math. 58, 364–376 (1936).

    Article  MathSciNet  Google Scholar 

  17. H.L. Turrittin, Asymptotic expansions of solutions of systems of ordinary linear differential equations containing a parameter. Contributions to the theory of nonlinear oscillations, Vol. 2, Princeton Univ. Press, 81–116 (1952).

  18. H.L. Turrittin, Asymptotic distribution of zeros for certain exponential sums. Amer. J. of Math. 66, 199–228 (1944).

    Article  MathSciNet  MATH  Google Scholar 

  19. M. Wolter, Über die Entwicklung nach. Eigenfunktionen N-irregulären. Eigenwertprobleme mit zerfallenden Randbedingungen. Math. Z. 178, 99–113 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  20. R. Mennicken and M. Möller, Boundary eigenvalue problems. Notas de Algebra y Analysis 14, 100 pages (1986), Bahia Bianca Argentinia.

    Google Scholar 

  21. R. Mennicken and M. Möller, Root functions of boundary eigenvalue operator, functions. Integral Equ. and Operator Theory 9, 237–265 (1986).

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Universität-GH-Duisburg, 4100, Duisburg, Lotharstr.65

    Gerhard Freiling

Authors
  1. Gerhard Freiling
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Freiling, G. Boundary value problems associated with multiple roots of the characteristic equation. Results. Math. 11, 44–62 (1987). https://doi.org/10.1007/BF03323258

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03323258

Keywords

Search

Navigation