Title:
|
On the transformation theory of ordinary second-order linear symmetric differential expressions (English) |
Author:
|
Everitt, William Norrie |
Language:
|
English |
Journal:
|
Czechoslovak Mathematical Journal |
ISSN:
|
0011-4642 (print) |
ISSN:
|
1572-9141 (online) |
Volume:
|
32 |
Issue:
|
2 |
Year:
|
1982 |
Pages:
|
275-306 |
Summary lang:
|
Russian |
. |
Category:
|
math |
. |
MSC:
|
34A25 |
MSC:
|
34B20 |
idZBL:
|
Zbl 0526.34026 |
idMR:
|
MR654062 |
DOI:
|
10.21136/CMJ.1982.101802 |
. |
Date available:
|
2008-06-09T14:48:14Z |
Last updated:
|
2020-07-28 |
Stable URL:
|
http://hdl.handle.net/10338.dmlcz/101802 |
. |
Reference:
|
[1] С. D. Ahlbrandt: Disconjugacy criteria for self-adjoint differential systems.J. Diff. Equations 6 (1969), 271-295. Zbl 0175.09301, MR 0244541, 10.1016/0022-0396(69)90018-7 |
Reference:
|
[2] N. I. Akhiezer, I. M. Glazman: Theory of linear operators in Hilbert space: Volume I.(Ungar; New York, 1961). MR 0264420 |
Reference:
|
[3] F. V. Atkinson: Discrete and continuous boundary problems.(Academic Press; New York, 1964). Zbl 0117.05806, MR 0176141 |
Reference:
|
[4] C. Bennewitz, W. N. Everitt: Some remarks on the Titchmarsh-Weyl $m$-coefficient.In: Tribute to Åke Pleijel: Proceedings of the Pleijel Conference, University of Uppsala (1979), 49-108. (Published by the Department of Mathematics, University of Uppsala, Sweden, in 1980). |
Reference:
|
[5] G. Birkhoff, Gian-Carlo Rota: Ordinary differential equations.(Ginn and Company, New York, 1962). MR 0138810 |
Reference:
|
[6] O. Borůvka: Linear differential transformations of the second order.(English Universities Press; London, 1971; translated from the German edition of 1967). MR 0463539 |
Reference:
|
[7] N. Dunford, J. T. Schwartz: Linear operators: Part II.(Interscience Publishers; New York, 1963). Zbl 0128.34803, MR 0188745 |
Reference:
|
[8] M. S. P. Eastham: Theory of ordinary differential equations.(Van Nostrand Reinhold Company; London, 1970). Zbl 0195.37001 |
Reference:
|
[9] M. S. P. Eastham: The spectral theory of periodic differential equations.(Scottish Academic Press; Edinburgh, 1973). Zbl 0287.34016 |
Reference:
|
[10] W. N. Everitt: On a property of the $m$-coefficient of a second-order linear differential equation.J. London Math. Soc. (2) 4 (1972), 443-457. Zbl 0262.34012, MR 0298104 |
Reference:
|
[11] W. N. Everitt: Integral inequalities and the Liouville transformation.Lecture Notes in Mathematics 415 (1974), 338-352. (Springer-Verlag; Heidelberg, 1974; edited by I. M. Michael and B. D. Sleeman). Zbl 0307.34013, MR 0419919, 10.1007/BFb0065546 |
Reference:
|
[12] W. N. Everitt: A note on the Dirichlet condition for second-order differential expressions.Canadian J. Math. XXVII (1916), 312-320. MR 0430391 |
Reference:
|
[13] W. N. Everitt: A general integral inequality associated with certain ordinary differential operators.Quaestiones Mathematicae 2 (1978), 479-494. Zbl 0396.26006, MR 0486761, 10.1080/16073606.1978.9631547 |
Reference:
|
[14] W. N. Everitt M. Giertz, J. B. McLeod: On the strong and weak limit-point classification of second-order differential expressions.Proc. London Math. Soc. (3) 29 (1974), 142-158. MR 0361255 |
Reference:
|
[15] W. N. Everitt, S. G. Halvorsen: On the asymptotic form of the Titchmarsh-Weyl $m$-coefficient.Applicable Analysis 8 (1978), 153 - 169. Zbl 0406.34047, MR 0523952, 10.1080/00036817808839223 |
Reference:
|
[16] W. N. Everitt, D. Race: On necessary and sufficient conditions for the existence of Carathéodory solutions of ordinary differential equations.Quaestiones Mathematicae 2 (1978), 507-512. Zbl 0392.34002, MR 0477222, 10.1080/16073606.1978.9631549 |
Reference:
|
[17] W. N. Everitt, A. Zettl: Generalized symmetric ordinary differential expressions I: the general theory.Nieuw Archief voor Wiskunde (3) XXVII (1979), 363-397. Zbl 0451.34009, MR 0553264 |
Reference:
|
[18] W. N. Everitt, A. Zettl: On a class of integral inequalities.J. London Math. Soc. (2) 17 (1978), 291-303. Zbl 0388.26007, MR 0477234, 10.1112/jlms/s2-17.2.291 |
Reference:
|
[19] E. Hille: Lectures on ordinary differential equations.(Addison-Wesley; London, 1969). Zbl 0179.40301, MR 0249698 |
Reference:
|
[20] D. B. Hinton: Limit point - limit circle criteria for $(py\sp{\prime} )\sp{\prime} +qy=\lambda ky$.Lecture Notes in Mathematics 415 (1974), 173 - 183. (Springer-Verlag; Heidelberg, 1974; edited by I. M. Michael and B. D. Sleeman). MR 0425236, 10.1007/BFb0065526 |
Reference:
|
[21] E. L. Ince: Ordinary differential equations.(Dover Publications, Inc.: New York, 1956; original edition, 1926). MR 0010757 |
Reference:
|
[22] H. Kalf: Remarks on some Dirichlet type results for semi-bounded Sturm-Liouville operators.Math. Ann. 210 (1974), 197-205. MR 0355177, 10.1007/BF01350583 |
Reference:
|
[23] M. A. Naimark: Linear differential operators: Part II.(Ungar; New York, 1968). Zbl 0227.34020 |
Reference:
|
[24] F. Neuman: On the Liouville transformation.Rendiconti di Matematica 3 (1970), 132-139. Zbl 0241.34005, MR 0273090 |
Reference:
|
[25] F. Neuman: On a problem of transformations between limit-point and limit-circle differential equations.Proc. Royal. Soc. Edinburgh 72 (1973/74), 187-193. MR 0385226 |
Reference:
|
[26] K. S. Ong: On the limit-point and limit-circle theory of a second-order differential equation.Proc. Royal Soc. Edinburgh 72 (1975), 245-256. MR 0393635 |
Reference:
|
[27] Å. Pleijel: Generalized Weyl circles.Lecture Notes in Mathematics 415 (1974), 211 - 226. (Springer-Verlag; Heidelberg, 1974; edited by I. M. Michael and B. D. Sleeman). Zbl 0301.34025, MR 0422741, 10.1007/BFb0065531 |
Reference:
|
[28] W. T. Reid: Ordinary differential equations.(Wiley and Sons, Inc.; New York, 1971). Zbl 0212.10901, MR 0273082 |
Reference:
|
[29] E. C. Titchmarsh: Eigenfunction expansions; Part I.(Oxford University Press, 1962). MR 0176151 |
Reference:
|
[30] R. Weinstock: Calculus of variations.(McGraw-Hill; New York, 1952), Zbl 0049.19503 |
Reference:
|
[31] A. Zettl: Formally self-adjoint quasi-differential operators.Rocky Mountain J. of Math. 5 (1975), 453-474. MR 0379976, 10.1216/RMJ-1975-5-3-453 |
. |