Annali di Matematica Pura ed Applicata

, Volume 89, Issue 1, pp 169–216 | Cite as

Existence of solutions to a linear integro-boundary-differential equation with additional conditions

  • O. Vejvoda
  • M. Tvrdy
Article

Summary

To a linear integro-boundary-differential equation(6.1) with rather general additional conditions(6.2) and(6.3) an adjoint problem is derived. This makes possible to state a classical solvability condition. Furthermore a Green’s matrix to the given problem is constructed. All solutions are sought as regular functions of bounded variation.

Keywords

Additional Condition Bounded Variation Regular Function Solvability Condition Adjoint Problem 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    M. E. Bounitzky,Sur la fonction de Green des équations différentielles linéaires ordinaires, J. Math. Pures Appl, 5 (1909), pp. 65–125.MATHGoogle Scholar
  2. [2]
    R. N. Bryan,A linear differential system with general linear boundary conditions, J. Diff. Equations, 5 (1969), pp. 38–48.CrossRefMATHMathSciNetGoogle Scholar
  3. [3]
    R. H. Cole,General boundary value problems for an ordinary linear differential system, Trans. Amer. Math. Soc., 111 (1964), pp. 521–550.CrossRefMATHMathSciNetGoogle Scholar
  4. [4]
    R. Conti,General boundary value problems for an ordinary linear differential equations, Boll. U. M. I., (3) vol. XXII (1967), pp. 135–178.MathSciNetGoogle Scholar
  5. [5]
    A. Halanay andA. Moro,A boundary value problem and its adjoint, Ann. di Mat. pura ed appl., (4) vol. LXXIX (1968), pp. 399–412.MathSciNetGoogle Scholar
  6. [6]
    T. H. Hildebrandt,On systems of linear differentio-Stieltjes-integral equations, Illinois J. Math., 3 (1959), pp. 352–373.MATHMathSciNetGoogle Scholar
  7. [7]
    —— ——,Introduction to the theory of integration, Academic Press, (1963), New York and London.MATHGoogle Scholar
  8. [8]
    W. R. Jones,Differential systems with integral boundary conditions, J. Diff. Equations, 3 (1967), pp. 191–202.CrossRefMATHGoogle Scholar
  9. [9]
    A. M. Krall,Nonhomogeneous differential operators, Michigan Math. J., 12 (1955) pp. 247–255.MathSciNetGoogle Scholar
  10. [10]
    —— ——,Differential operators and their adjoints under integral and multiple point boundary conditions, J. Diff. Equations, 4 (1968), pp. 327–336.CrossRefMATHMathSciNetGoogle Scholar
  11. [11]
    -- --,Differential-boundary equations and associated boundary value problems, Proc. US-Japan Seminar on Differential and Functional Equations, University of Minesota, Minneapolis, June 26–30 1967; W.A. Benjamin, Inc. (1967), pp. 463–472.Google Scholar
  12. [12]
    R. D. Moyer,The adjoints of ordinary differential operators, J. Diff. Equations, 4 (1968), pp. 337–349.CrossRefMATHMathSciNetGoogle Scholar
  13. [13]
    M. Pagni,Equazioni differenziali lineari e problemi al contorno c n condizioni integrali, Rend. Sem. Mat. Univ. Padova, 24 (1955), pp. 245–264.MATHMathSciNetGoogle Scholar
  14. [14]
    D. H. Tucker,Boundary value problems for linear differential systems, SIAM J. Appl. Math., 17 (1969), pp. 769–783.CrossRefMATHMathSciNetGoogle Scholar
  15. [15]
    D. Wexler,On boundary value problems for an ordinary linear differential system, Ann. di Mat. pura ed appl., (4) vol. LXXX (1968), pp. 123–134.MathSciNetGoogle Scholar
  16. [16]
    W. M. Whyburn,Differential equations with general boundary conditions, Bull. Amer. Math. Soc., 48 (1942), pp. 692–704.MATHMathSciNetCrossRefGoogle Scholar
  17. [17]
    V. I. Smirnov,A course of higher mathematics, vol. III, Part. 1, Intern. Series o, Monographs in pure and appl. Math., vol. 59, The Macmillan Company.Google Scholar
  18. [18]
    R. N. Bryan,A nonhomogeneous linear differential system with interface conditions, Proc. Amer. Math. Soc., 22 (1969), pp. 270–276.CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Nicola Zanichelli Editore 1971

Authors and Affiliations

  • O. Vejvoda
  • M. Tvrdy

There are no affiliations available

Personalised recommendations