An integral condition of oscillation for equation y ' ' ' + p ( t ) y ' + q ( t ) y = 0 with nonnegative coefficients

Anton Škerlík

Archivum Mathematicum (1995)

  • Volume: 031, Issue: 2, page 155-161
  • ISSN: 0044-8753

Abstract

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Our aim in this paper is to obtain a new oscillation criterion for equation y ' ' ' + p ( t ) y ' + q ( t ) y = 0 with a nonnegative coefficients which extends and improves some oscillation criteria for this equation. In the special case of equation (*), namely, for equation y ' ' ' + q ( t ) y = 0 , our results solve the open question of C h a n t u r i y a .

How to cite

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Škerlík, Anton. "An integral condition of oscillation for equation $y^{\prime \prime \prime }+p(t)y^{\prime }+q(t)y=0$ with nonnegative coefficients." Archivum Mathematicum 031.2 (1995): 155-161. <http://eudml.org/doc/247676>.

@article{Škerlík1995,
abstract = {Our aim in this paper is to obtain a new oscillation criterion for equation \[ y^\{\prime \prime \prime \}+ p(t)y^\{\prime \} + q(t)y = 0 \] with a nonnegative coefficients which extends and improves some oscillation criteria for this equation. In the special case of equation (*), namely, for equation $ y^\{\prime \prime \prime \}+ q(t)y = 0$, our results solve the open question of $Chanturiya$.},
author = {Škerlík, Anton},
journal = {Archivum Mathematicum},
keywords = {nonoscillatory and oscillatory solution; second order Riccati equation; third order linear differential equation; oscillation},
language = {eng},
number = {2},
pages = {155-161},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {An integral condition of oscillation for equation $y^\{\prime \prime \prime \}+p(t)y^\{\prime \}+q(t)y=0$ with nonnegative coefficients},
url = {http://eudml.org/doc/247676},
volume = {031},
year = {1995},
}

TY - JOUR
AU - Škerlík, Anton
TI - An integral condition of oscillation for equation $y^{\prime \prime \prime }+p(t)y^{\prime }+q(t)y=0$ with nonnegative coefficients
JO - Archivum Mathematicum
PY - 1995
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 031
IS - 2
SP - 155
EP - 161
AB - Our aim in this paper is to obtain a new oscillation criterion for equation \[ y^{\prime \prime \prime }+ p(t)y^{\prime } + q(t)y = 0 \] with a nonnegative coefficients which extends and improves some oscillation criteria for this equation. In the special case of equation (*), namely, for equation $ y^{\prime \prime \prime }+ q(t)y = 0$, our results solve the open question of $Chanturiya$.
LA - eng
KW - nonoscillatory and oscillatory solution; second order Riccati equation; third order linear differential equation; oscillation
UR - http://eudml.org/doc/247676
ER -

References

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  7. Qualitative behavior of solutions of a third order nonlinear differential equation, Pacific J. Math. 27 (1968), 507–526. (1968) Zbl0172.11703MR0240389
  8. Oscillation of solutions of third-order linear ordinary differential equations, Differencialnye Uravneniya 27 (1991), no. 3, 4, 452–460, 611–618. (in Russian) (1991) MR1109137
  9. On the oscillation of solutions of the equation d m / d t m + a ( t ) | u | n s i g n u = 0 , Mat. Sb. 65 (1964), 172–187. (in Russian) (1964) Zbl0135.14302MR0173060
  10. Some singular value problems for ordinary differential equations, University Press, Tbilisi (1975). (in Russian) (1975) MR0499402
  11. The behavior of solutions of the differential equation y ' ' ' + p ( x ) y ' + q ( x ) y = 0 , Pacific J. Math. 17 (1966), 435–466. (1966) Zbl0143.31501MR0193332
  12. Oscillation criteria for third-order linear differential equations, Mat. Časopis 25 (1975), 231–244. (1975) Zbl0309.34028MR0412521
  13. Integral criteria of oscillation for a third order linear differential equation, Math. Slovaca (to appear). (to appear) MR1387057
  14. Oscillation theorems for third order nonlinear differential equations, Math. Slovaca 42 (1992), 471–484. (1992) MR1195041
  15. Oscillatory properties of solutions of a third order nonlinear differential equations, Math.Slovaca 26 (1976), 217–227. (in Russian) (1976) 
  16. Comparison and Oscillation Theory of Linear Differential Equations, Academic Press, New York-London, 1968. (1968) Zbl0191.09904MR0463570

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