| Title:
|
Some classes of linear $n$th-order differential equations (English) |
| Author:
|
Šeda, Valter |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
33 |
| Issue:
|
1 |
| Year:
|
1997 |
| Pages:
|
157-165 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Sufficient conditions for the $n$-th order linear differential equation are derived which guarantee that its Cauchy function $K$, together with its derivatives ${\partial ^i K}\over {\partial t^i}$, $i=1,\dots ,n-1$, is of constant sign. These conditions determine four classes of the linear differential equations. Further properties of these classes are investigated. (English) |
| Keyword:
|
Cauchy function |
| Keyword:
|
Čaplygin comparison theorem |
| Keyword:
|
monotonic solutions |
| Keyword:
|
regularity of bands |
| MSC:
|
34A40 |
| MSC:
|
34D05 |
| idZBL:
|
Zbl 0914.34011 |
| idMR:
|
MR1464310 |
| . |
| Date available:
|
2008-06-06T21:33:01Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107606 |
| . |
| Reference:
|
[1] O. Borůvka: Lineare Differentialtransformationen 2.Ordnung.VEB, Berlin, 1967. |
| Reference:
|
[2] M. Gera: Bedingungen der Nichtoszillationsfähigkeit für die lineare Differentialgleichung dritter Ordnung $ y^{\prime \prime \prime }+p_1(x)y^{\prime \prime } +p_2(x)y^{\prime }+p_3(x)y=0 $.Acta F. R. N. Univ. Comen.-Mathematica XXIII (1969), 13–34. Zbl 0216.11303, MR 0291554 |
| Reference:
|
[3] M. Gera: Bedingungen der Nicht-oszillationsfähigkeit und der Oszillationsfähigkeit für die lineare Differentialgleichung dritter Ordnung.Mat. časop. 21 (1971), 65–80. Zbl 0216.11302, MR 0304769 |
| Reference:
|
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| Reference:
|
[5] M. Greguš: Third Order Linear Differential Equations.D. Reidel Publ. Co., Dordrecht, 1987. MR 0882545 |
| Reference:
|
[6] Ph. Hartman: Ordinary Differential Equations.J. Wiley and Sons, New York, 1964. Zbl 0125.32102, MR 0171038 |
| Reference:
|
[7] I. T. Kiguradze, T. A. Čanturija: Asymptotical Properties of Solutions of Nonautonomous Ordinary Differential Equations.Nauka, Moscow, 1990. (Russian) |
| Reference:
|
[8] M. A. Krasnoseľskij: Approximate Solution of Operator Equations.Nauka, Moscow, 1969. (Russian) MR 0259635 |
| Reference:
|
[9] F. Neuman: Global Properties of Linear Ordinary Differential Equations.Academia, Praha, 1991. Zbl 0784.34009, MR 1192133 |
| Reference:
|
[10] R. Rabczuk: Foundations of Differential Inequalities.Pan. Wydav. Nauk., Warsaw, 1976. (Polish) MR 0457827 |
| Reference:
|
[11] J. Regenda: Oscillatory and Nonoscillatory Properties of Solutions of the Differential Equation $y^{(4)}+P(t)y"+Q(t)y=0$.Math. Slovaca 28 (1978), 329–342. MR 0534812 |
| Reference:
|
[12] E. Rovderová: Existence of a Monotone Solution of a Nonlinear Differential Equation.J. Math. Anal. Appl. 192 (1995), 1–15. MR 1329409 |
| Reference:
|
[13] V. Šeda: On a Class of Linear $n$-th Order Differential Equations.Czech. Math. J. 39(114) (1989), 350–369. |
| . |
