Advertisement

Square integrable solutions of Lp perturbations of second order linear differential equations

  • James S. W. Wong
Invited Lectures
Part of the Lecture Notes in Mathematics book series (LNM, volume 415)

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    R. Bellman, "A stability principle of solutions of linear differential equations", Duke Math. J., 11(1944), 513–516.MathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    R. Bellman, Stability Theory of Differential Equations, McGraw-Hill, New York, 1953.zbMATHGoogle Scholar
  3. [3]
    J. S. Bradley, "Comparison Theorems for the square integrability of solutions of (r(t)y′)′ + q(t)y = f(t,y)″, Glasgow Math. J., 13(1972), 75–79.MathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    N. Dunford and J.T. Schwartz, Linear Operators, Part II: Spectral Theory, Interscience, New York, 1963.zbMATHGoogle Scholar
  5. [5]
    W. N. Everitt and J. Chaudhuri, "On the spectrum of ordinary second-order differential operators", Proc. Royal Soc. Edinburgh, 68(1969), 95–119.zbMATHGoogle Scholar
  6. [6]
    W. N. Everitt, M. Giertz, and J. Weidmann, "Some remarks on a separation and limit point criterion of second order ordinary differential expressions", Math. Ann., 200(1973), 335–346.MathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    W. N. Everitt, D.B. Hinton and J.S.W. Wong, "On the strong limit-n classification of linear ordinary differential expressions of order 2n", Proc. London Math. Soc., (1974), (to appear).Google Scholar
  8. [8]
    P. Hartman, "The number of L2-solutions of x″+p(t)x=O", Amer. J. Math., 73(1951), 635–645.MathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    P. Hartman and A. Wintner, "A criterion for the nondegeneracy of the wave equation", Amer. J. Math., 71(1949), 206–213.MathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    G. Hellwig, Differential Operators of Mathematical Physics, Addison-Wesley, Reading, Massachusetts, 1964.CrossRefzbMATHGoogle Scholar
  11. [11]
    E. Hille, Lectures on Ordinary Differential Equations, Addison-Wesley, Reading, Massachusetts, 1969.zbMATHGoogle Scholar
  12. [12]
    H. Kurss, "A limit point criterion for nonoscillatory Sturm-Liouville differential operators", Proc. Amer. Math. Soc., 18(1967), 445–449.MathSciNetCrossRefzbMATHGoogle Scholar
  13. [13]
    N. Levinson, "Criteria for the limit point case for second order linear differential operators", Casopis Pest. Mat. Fys., 74(1949), 17–20.MathSciNetzbMATHGoogle Scholar
  14. [14]
    A. Yu Levin, "Nonoscillation of solutions of the equation x(n) + p1(t) x(n−1) +...... + pn(t)x = 0", Russian Math. Survey, 24(1969), 43–99.CrossRefGoogle Scholar
  15. [15]
    M. A. Naimark, Linear Differential Operators, part II, Ungar, New York, 1968.zbMATHGoogle Scholar
  16. [16]
    W. T. Patula and P. Waltman, "Limit point classification of second order linear differential equations", J. London Math. Soc., (1973), to appear.Google Scholar
  17. [17]
    W. T. Patula and J.S. W. Wong, "An LP-analogue of the Weyl's alternative", Math. Ann., 197(1972), 9–27.MathSciNetCrossRefzbMATHGoogle Scholar
  18. [18]
    E.C. Titchmarsh, "On the uniqueness of the Green's function associated with a second order differential equation", Canadian J. Math., 1(1949), 191–198.MathSciNetCrossRefzbMATHGoogle Scholar
  19. [19]
    E.C. Titchmarsh, Eigenfunction expansions associated with second order differential equations, (Second edition), Oxford Press, Oxford, 1962.zbMATHGoogle Scholar
  20. [20]
    H. Weyl, "Uber gewohnliche Differential-gleichungen mit Singularitaten und die zugehorige Entwicklung will kurlicker Functionen", Math. Ann., 68(1910), 220–269.MathSciNetCrossRefGoogle Scholar
  21. [21]
    J.S.W. Wong, "Remarks on the limit circle classification of second order differential operators", Quarterly J. Math., 24(1973), 423–425.MathSciNetCrossRefzbMATHGoogle Scholar
  22. [22]
    J.S.W. Wong, "On L2-solutions of linear ordinary differential equations", Duke Math. J., 38(1971), 93–97.MathSciNetCrossRefGoogle Scholar
  23. [23]
    J.S.W. Wong and A. Zettl, "On the limit point classification of second order differential equations", Math. Zeitschrift, 132(1973), 297–304.MathSciNetCrossRefzbMATHGoogle Scholar
  24. [24]
    A. Zettl, "A note on square integrable solutions of linear differential equations", Proc. Amer. Math. Soc., 21(1969), 671–672.CrossRefzbMATHGoogle Scholar
  25. [25]
    A. Zettl, "Square integrable solutions of Ly=f(t,y)", Proc. Amer. Math. Soc., 26(1970), 635–639.MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1974

Authors and Affiliations

  • James S. W. Wong

There are no affiliations available

Personalised recommendations