On an oscillation criterion of Hartman, Wintner and Potter

Erhard Heil

Archivum Mathematicum (1979)

  • Volume: 015, Issue: 2, page 81-91
  • ISSN: 0044-8753

How to cite

top

Heil, Erhard. "On an oscillation criterion of Hartman, Wintner and Potter." Archivum Mathematicum 015.2 (1979): 81-91. <http://eudml.org/doc/17995>.

@article{Heil1979,
author = {Heil, Erhard},
journal = {Archivum Mathematicum},
keywords = {oscillation criterion},
language = {eng},
number = {2},
pages = {81-91},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {On an oscillation criterion of Hartman, Wintner and Potter},
url = {http://eudml.org/doc/17995},
volume = {015},
year = {1979},
}

TY - JOUR
AU - Heil, Erhard
TI - On an oscillation criterion of Hartman, Wintner and Potter
JO - Archivum Mathematicum
PY - 1979
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 015
IS - 2
SP - 81
EP - 91
LA - eng
KW - oscillation criterion
UR - http://eudml.org/doc/17995
ER -

References

top
  1. Breuer S., Gottlieb D., Separation of roots and oscillation in ordinary linear differential equations of second order, Proc. Amer. Math. Soc. 29 (1971), 487-493. (1971) Zbl0224.34024MR0276545
  2. Caratheodory C., Vorlesungen über reelle Funktionen, 2. Aufl. Teubner Leipzig 1927. (1927) Zbl53.0225.16
  3. Etgen G. J., Pawlowski J. F., Oscillation criteria for second order self adjoint differential systems, Pacific J. Math. 66 (1976) 99-110. (1976) Zbl0355.34017MR0440147
  4. Fite W. B., Concerning the zeros of the solutions of certain differential equations, Trans. Amer. Math. Soc. 19 (1917), 341-352. (1917) Zbl46.0702.02MR1501107
  5. Gagliardo E., Sul comportamento asintotico degli integrali dell’equazione differenziale y " + A ( x ) y = 0 con A ( x ) 0 , Boll. Unione Mat. Ital. (3) 8 (1953), 177-185. (1953) Zbl0051.32002MR0056779
  6. Guggenheimer H., Hill equations with coexisting periodic solutions, J. Diff. Equations 5 (1969), 159-166. (1969) Zbl0186.41003MR0239193
  7. Hartman P., Wintner A., On non-conservative linear oscillators of low frequency, Amer. J. Math. 70 (1948), 529-539. (1948) Zbl0037.19002MR0026736
  8. Kreith K., Oscillation theory, Lecture Notes in Math. 324, Springer-Verlag Berlin, Heidelberg, New York 1973. (1973) Zbl0258.35001
  9. Laugwitz D., Differentialgeometrie in Vektorräumen, Vieweg Braunschweig 1965. (1965) Zbl0139.14904MR0182924
  10. Leighton W., Principal quadratic functionals and self adjoint second-order differential equations, Proc. Nat. Acad. Sci. 35 (1949) 192-193. (1949) Zbl0032.34603MR0030672
  11. Leighton W., On self adjoint differential equations of second order, J. London Math. Soc. 27 (1952), 37-47. (1952) Zbl0048.06503MR0046506
  12. Moore R. A., The behavior of solutions of a linear differential equation of second order, Pacific J. Math. 5 (1955), 125-145. (1955) MR0068690
  13. Neuman F., Centroaffine invariants of plane curves in connection with the theory of the second order linear differential equations, Archivum Math. (Brno) 4 (1968), 201-216. (1968) Zbl0218.34007MR0267512
  14. Opial Z., Sur une critère d’oscillation des integrales de l’equation différentielle ( Q ( t ) x ' ) ' + f ( t ) x = 0 , Ann. Polon. Math. 6 (1959/1960), 99-104. (1959) Zbl0085.30403MR0104876
  15. Pfaff R., Zur Theorie der gewöhnlichen linearen Differentialgleichung zweiter Ordnung mit Distributionskoeffizient, Dissertation Darmstadt 1978. (1978) MR0481259
  16. Potter R. L., On self-adjoint differential equations of second order, Pacific J. Math. 3 (1953),. 467-491. (1953) Zbl0051.06502MR0056156
  17. Ráb M., Kriterien für die Oszillation der Lösungen der Differentialgleichung [ p ( x ) y ' ] ' + q ( x ) y = 0 , Časopis Pěst. Mat. 84 (1959), 335-370. (1959) Zbl0087.29505MR0114964
  18. Swanson C. A., Comparison and oscillation theory of linear differential equations, Academic Press New York, London 1968. (1968) Zbl0191.09904MR0463570
  19. Willet D., Classification of second order linear differential equations with respect to oscillation, In: Lectures on ordinary differential equations. Ed. R. McKelvey, Academic Press New York, London 1970. (1970) MR0280800
  20. Wintner A., A criterion of oscillatory stability, Quarterly Appl. Math. 7 (1949), 115-117. (1949) Zbl0032.34801MR0028499

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.