Oscillatory properties of fourth order self-adjoint differential equations
Archivum Mathematicum (2004)
- Volume: 040, Issue: 4, page 457-469
- ISSN: 0044-8753
Access Full Article
top
Abstract
topHow to cite
topFišnarová, Simona. "Oscillatory properties of fourth order self-adjoint differential equations." Archivum Mathematicum 040.4 (2004): 457-469. <http://eudml.org/doc/249304>.
@article{Fišnarová2004,
abstract = {Oscillation and nonoscillation criteria for the self-adjoint linear differential equation \[ (t^\alpha y^\{\prime \prime \})^\{\prime \prime \}-\frac\{\gamma \_\{2,\alpha \}\}\{t^\{4-\alpha \}\}y=q(t)y,\quad \alpha \notin \lbrace 1, 3\rbrace \,, \]
where \[ \gamma \_\{2,\alpha \}=\frac\{(\alpha -1)^2(\alpha -3)^2\}\{16\}\]
and $q$ is a real and continuous function, are established. It is proved, using these criteria, that the equation \[\left(t^\alpha y^\{\prime \prime \}\right)^\{\prime \prime \}-\left(\frac\{\gamma \_\{2,\alpha \}\}\{t^\{4-\alpha \}\} + \frac\{\gamma \}\{t^\{4-\alpha \}\ln ^2 t\}\right)y = 0\]
is nonoscillatory if and only if $\gamma \le \frac\{\alpha ^2-4\alpha +5\}\{8\}$.},
author = {Fišnarová, Simona},
journal = {Archivum Mathematicum},
keywords = {self-adjoint differential equation; oscillation and nonoscillation criteria; variational method; conditional oscillation; self-adjoint differential equation},
language = {eng},
number = {4},
pages = {457-469},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Oscillatory properties of fourth order self-adjoint differential equations},
url = {http://eudml.org/doc/249304},
volume = {040},
year = {2004},
}
TY - JOUR
AU - Fišnarová, Simona
TI - Oscillatory properties of fourth order self-adjoint differential equations
JO - Archivum Mathematicum
PY - 2004
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 040
IS - 4
SP - 457
EP - 469
AB - Oscillation and nonoscillation criteria for the self-adjoint linear differential equation \[ (t^\alpha y^{\prime \prime })^{\prime \prime }-\frac{\gamma _{2,\alpha }}{t^{4-\alpha }}y=q(t)y,\quad \alpha \notin \lbrace 1, 3\rbrace \,, \]
where \[ \gamma _{2,\alpha }=\frac{(\alpha -1)^2(\alpha -3)^2}{16}\]
and $q$ is a real and continuous function, are established. It is proved, using these criteria, that the equation \[\left(t^\alpha y^{\prime \prime }\right)^{\prime \prime }-\left(\frac{\gamma _{2,\alpha }}{t^{4-\alpha }} + \frac{\gamma }{t^{4-\alpha }\ln ^2 t}\right)y = 0\]
is nonoscillatory if and only if $\gamma \le \frac{\alpha ^2-4\alpha +5}{8}$.
LA - eng
KW - self-adjoint differential equation; oscillation and nonoscillation criteria; variational method; conditional oscillation; self-adjoint differential equation
UR - http://eudml.org/doc/249304
ER -
References
top- Coppel W. A., Disconjugacy, Lectures Notes in Math., No. 220, Springer Verlag, Berlin-Heidelberg 1971. (1971) Zbl0224.34003MR0460785
- Došlý O., Nehari-type oscillation criteria for self-adjoint linear equations, J. Math. Anal. Appl. 182 (1994), 69–89. (1994) MR1265883
- Došlý O., Oscillatory properties of fourth order Sturm-Liouville differential equations, Acta Univ. Palack. Olomuc. Fac. Rerum. Natur. Math. 41 (2002), 49–59. Zbl1055.34065MR1967340
- Došlý O., Osička J., Oscillation and nonoscillation of higher order self-adjoint differential equations, Czechoslovak Math. J. 52 (127) (2002), 833-849. MR1940063
- Došlý O., Osička J., Oscillatory properties of higher order Sturm-Liouville differential equations, Studies Univ. Žilina, Math. Ser. 15 (2002), 25–40. Zbl1062.34034MR1980760
- Glazman I. M., Direct Methods of Qualitative Anylysis of Singular Differential Operators, Davey, Jerusalem 1965. (1965)
- Hinton D. B., Lewis R. T., Discrete spectra criteria for singular differential operators with middle terms, Math. Proc. Cambridge Philos. Soc. 77 (1975), 337–347. (1975) Zbl0298.34018MR0367358
NotesEmbed ?
topYou 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.