Criteria for the oscilation of solution of differential equation [ p ( x ) y ' ] ' + q ( x ) y = 0

Miloš Ráb

Časopis pro pěstování matematiky (1959)

  • Volume: 084, Issue: 3, page 335-370
  • ISSN: 0528-2195

How to cite

top

Ráb, Miloš. "Kriterien für die Oszillation der Lösungen der Differentialgleichung $[p(x)y^{\prime }]^{\prime }+q(x)y=0$." Časopis pro pěstování matematiky 084.3 (1959): 335-370. <http://eudml.org/doc/20680>.

@article{Ráb1959,
author = {Ráb, Miloš},
journal = {Časopis pro pěstování matematiky},
keywords = {ordinary differential equations},
language = {ger},
number = {3},
pages = {335-370},
publisher = {Mathematical Institute of the Czechoslovak Academy of Sciences},
title = {Kriterien für die Oszillation der Lösungen der Differentialgleichung $[p(x)y^\{\prime \}]^\{\prime \}+q(x)y=0$},
url = {http://eudml.org/doc/20680},
volume = {084},
year = {1959},
}

TY - JOUR
AU - Ráb, Miloš
TI - Kriterien für die Oszillation der Lösungen der Differentialgleichung $[p(x)y^{\prime }]^{\prime }+q(x)y=0$
JO - Časopis pro pěstování matematiky
PY - 1959
PB - Mathematical Institute of the Czechoslovak Academy of Sciences
VL - 084
IS - 3
SP - 335
EP - 370
LA - ger
KW - ordinary differential equations
UR - http://eudml.org/doc/20680
ER -

References

top
  1. Barret J. H., Behavior of solutions of second order selfadjoint differential equations, Proc. Amer. Math. Soc. 6 (1955), 247-251. (1955) MR0070804
  2. Bohl P., Über eine Differentialgleichung der Störungstheorie, J. Reine Angew. Math. 131 (1906), 268-321. (1906) 
  3. Bôcher M., Application of a method of d’Alembert to the proof of Sturm’s theorem of comparison, Trans. Amer. Math. Soc. 1 (1900), 414-420. (1900) MR1500548
  4. Bôcher M., An elementary proof of a theorem of Sturm, Trans. Amer. Math. Soc. 2 (1901), 150-151. (1901) MR1500561
  5. Borůvka O., Théorie analytique et constructive des transformations différentielles linéaires du second ordre, Bull. Math. Soc. Roum. Sci. 1 (49), No 2 (1957), 125-130. (1957) MR0104857
  6. Eлъшuн M. И., Meтoд фaз и клaccичecкий мeтoд cpaвнeния, Дoкл. Aкaд. Hayк CCCP 68 (1949), 813-816. (1949) 
  7. Fite W. B., Concerning the zeros of the solutions of certain differential equations, Trans. Amer. Math. Soc. 19 (1918), 341-352. (1918) MR1501107
  8. Gagliardo E., Sui criteгi di oszillatione per gli integrali di un equazione differenziale lineare del secondo ordine, Boll. Un. Mat. Ital., ser. III, IX (1954), 177-189. (1954) MR0064231
  9. Landolino G., Sul teorema di confronto di Sturm, Boll. Un. Mat. Ital., ser. III, 2 (1947), 16-19. (1947) Zbl0031.21401MR0021196
  10. Hartman P., On linear second order differential equations with small coefficients, Amer. J. Math. LXXIII (1951), 955-962. (1951) MR0045896
  11. Hartman P., On non oscillatory linear differential equations of second order, Amer. J. Math. LXXIV (1952), 389-400. (1952) Zbl0048.06602MR0048667
  12. Hartman P., On the linear logarithmico-exponential differential equation of the second order, Amer. J. Math. LXX (1948), 764-779. (1948) Zbl0035.18302MR0027926
  13. Hartman P., Wintner A., On non conservative linear oscillators of low frequency, Amer. J. Math. LXX (1948), 529-539. (1948) Zbl0037.19002MR0026736
  14. Hille E., Non-oscillation theorems, Trans. Amer. Math. Soc. 64 (1948), 234-252. (1948) Zbl0031.35402MR0027925
  15. Ielchin M., Sur le problème d’oscillation pour l’équation différentielle lineaire du deuxième ordre, C. R. (Doklady) Acad. Sci. URSS 18 (1938), 141-145. (1938) Zbl0019.30402
  16. Kamke E., Über Sturms Vergleichssätze für homogene lineare Differentialgleichungen zweiter Ordnung und Systeme von zwei Differentialgleichungen erster Ordnung, Math. Z. 47 (1940), 788-795. (1940) MR0014524
  17. Kamke E., A new proof of Sturm’s comparison theorems, Amer. Math. Monthly 46 (1939), 417-421. (1939) Zbl0061.17803MR0000326
  18. Kneser A., Untersuchungen über die reellen Nullstellen der Integrale linearer Differentialgleichungen, Math. Ann. 42 (1893), 409-435. MR1510784
  19. Koндpamьeв B. Л., Дocтaтoчныe ycлoвия нeкoлeблeмнocти и кoлeблeмocти peшeний ypaвнeния y" + p(x) y = 0, Дoкл. Aкaд. Hayк CCCP 113 (1957), 742-745. (1957) 
  20. Laitoch M., Sur une théorie des critères comparatifs sur l’oscillation des intégrales de l’équation différentielle u" = P(x) u, Spisy Přír. Fak. MU Brno, 365 (1955), 255-267. (1955) MR0082015
  21. Leighton W., On self-adjoint differential equations of second order, J. London Math. Soc. 27 (1952), 37-47. (1952) Zbl0048.06503MR0046506
  22. Leighton W., On self-adjoint differential equations of second order, Proc. Nat. Acad. Sci. U. S. A. 35 (1949), 656-657. (1949) MR0032064
  23. Leighton W., Principal quadratic functionals and self-adjoint second-order differential equations, Proc. Nat. Acad. Sci. U. S. A. 35 (1949), 192-193. (1949) Zbl0032.34603MR0030672
  24. Leighton W., The detection of the oscillation of solutions of a second order linear differential equation, Duke Math. J. 17 (1950), 57-62. (1950) Zbl0036.06101MR0032065
  25. Mikusiński J. G., On Fite’s oscillation theorems, Colloq. Math. II (1949), 34-39. (1949) 
  26. Moore R., The behavior of solutions of a linear differential equation of second order, Pacific J. Math. V (1955), 125-145. (1955) MR0068690
  27. Nehari Z., Oscillation criteria for second-order linear differential equations, Trans. Amer. Math. Soc. 85 (1957), 428-445. (1957) Zbl0078.07602MR0087816
  28. Oakley C. O., A note on the metods of Stuгm, Ann. of Math., ser. II, 31 (1930), 660-662. (1930) MR1502970
  29. Olech C, Opial Z., Ważewski T., Sur le problème d’oscillation des intégrales de l’équation y" + g(t) y = 0, Bull. Acad. Polon. Sci., cl. III, V (1957), 621-626. (1957) 
  30. Пemponaвлoвcкaя P. B., О кoлeбaтeльнocти peшeний ypaвнeния u" + p(x) u = 0, Дoкл. Aкaд. Hayк CCCP 105 (1955), 29-31. (1955) 
  31. Potter B. L., On self-adjoint differential equations of second order, Pacific J. Math. 3 (1953), 467-491. (1953) Zbl0051.06502MR0056156
  32. Prüfer H., Neue Herleitung der Sturm-Liouvilleschen Reihenentwicklung stetiger Funktionen, Math. Ann. 95 (1926), 499-518. (1926) MR1512291
  33. Putnam C. R., An oscillation criterion involving a minimum principle, Duke Math. J. 16 (1949), 633-636. (1949) Zbl0037.34302MR0033415
  34. Putnam C. R., Note on some oscillation criteria, Proc. Amer. Math. Soc. 6 (1955), 950-952. (1955) Zbl0067.06202MR0074613
  35. Ráb M., Poznámka k otázce o oscilačních vlastnostech řešení diferenciální rovnice y" + A(x) y = 0, Časopis pro pëst. mat. 82 (1957), 342 - 348. (1957) 
  36. Reid W. T., A comparison theorem for self-adjoint differential equations of second order, Ann. of Math. 65 (1957), 197-202. (1957) Zbl0077.08604MR0092045
  37. Coбoл И. M., Иccлeдoвaниe acимптoтичecкoгo пoвeдeния peшeний линeйнoгo диффepeнциaльнoгo ypaвнeния втopoгo пopядкa пpи пoмoщи пoляpныx кoopдинaт, Maт. Cб. 28 (70), (1951), 707-714. (1951) 
  38. Sturm C., Sur les Équations différentielles linéaires du second ordre, J. Math. Pures Appl. 1 (1836), 106-186. 
  39. Wintner A., A criterion of oscillatory stability, Quart. Appl. Math. VII (1949), 115-117. (1949) Zbl0032.34801MR0028499
  40. Wintner A., On the non existence of conjugate points, Amer. J. Math. LXXIII (1951), 368-380. (1951) MR0042005
  41. Wintner A., On the comparison theorem of Kneser-Hille, Math. Scand. 5 (1957) 2, 255-260. (1957) Zbl0080.29801MR0096867
  42. Zlámal M., Oscillations criterions, Časopis pro pӗst. mat. 75 (1950), 213-218. (1950) 
  43. Зyбoвa A. Ф., O кoлeбaнияx peшeний ypaвнeния втopoгo пopядкa, Becтник Лeнингpaд. Унив. 211 (1957) 1, 168-174. (1957) 

Citations in EuDML Documents

top
  1. Jozef Rovder, Niektoré vlastnosti diferenciálnej rovnice y ' ' + f ( x ) | y | = 0
  2. Milan Gera, Bedingungen für die Existenz oszillatorischer Lösungen der Gleichung x ' ' ' + a ( t ) x ' ' + b ( t ) x ' + c ( t ) x = 0 , c ( t ) > = 0
  3. Valter Šeda, On nonlinear differential systems with deviating arguments
  4. Miloš Ráb, Les développements asymptotiques des solutions de l’équation ( p y ' ) ' + q y = 0
  5. Erhard Heil, On an oscillation criterion of Hartman, Wintner and Potter
  6. Miloš Ráb, Asymptotische Formeln für die Lösungen der Differentialgleichung y ' ' + q ( x ) y = 0
  7. Zuzana Došlá, Jan Slovák, 100 let matematiky na Masarykově univerzitě
  8. Ivan Kiguradze, On the oscillatory and monotone solutions of ordinary differential equations

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.