Some classes of linear n th-order differential equations

Valter Šeda

Archivum Mathematicum (1997)

  • Volume: 033, Issue: 1-2, page 157-165
  • ISSN: 0044-8753

Abstract

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Sufficient conditions for the n -th order linear differential equation are derived which guarantee that its Cauchy function K , together with its derivatives ∂ i K ∂ t i , i = 1 , ⋯ , n - 1 , is of constant sign. These conditions determine four classes of the linear differential equations. Further properties of these classes are investigated.

How to cite

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Šeda, Valter. "Some classes of linear $n$th-order differential equations." Archivum Mathematicum 033.1-2 (1997): 157-165. <http://eudml.org/doc/248024>.

@article{Šeda1997,
abstract = {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.},
author = {Šeda, Valter},
journal = {Archivum Mathematicum},
keywords = {Cauchy function; Čaplygin comparison theorem; monotonic solutions; regularity of bands; Cauchy function; Čaplygin comparison theorem; monotonic solutions; regularity of bands},
language = {eng},
number = {1-2},
pages = {157-165},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Some classes of linear $n$th-order differential equations},
url = {http://eudml.org/doc/248024},
volume = {033},
year = {1997},
}

TY - JOUR
AU - Šeda, Valter
TI - Some classes of linear $n$th-order differential equations
JO - Archivum Mathematicum
PY - 1997
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 033
IS - 1-2
SP - 157
EP - 165
AB - 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.
LA - eng
KW - Cauchy function; Čaplygin comparison theorem; monotonic solutions; regularity of bands; Cauchy function; Čaplygin comparison theorem; monotonic solutions; regularity of bands
UR - http://eudml.org/doc/248024
ER -

References

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  2. Bedingungen der Nichtoszillationsfähigkeit für die lineare Differentialgleichung dritter Ordnung y ' ' ' + p 1 ( x ) y ' ' + p 2 ( x ) y ' + p 3 ( x ) y = 0 , Acta F. R. N. Univ. Comen.-Mathematica XXIII (1969), 13–34. (1969) Zbl0216.11303MR0291554
  3. Bedingungen der Nicht-oszillationsfähigkeit und der Oszillationsfähigkeit für die lineare Differentialgleichung dritter Ordnung, Mat. časop. 21 (1971), 65–80. (1971) Zbl0216.11302MR0304769
  4. Einige oszillatorische Eigenschaften der Lösungen der Differentialgleichung dritter Ordnung y ' ' ' + p ( x ) y ' + q ( x ) y = 0 , Scripta Fac. Sci. Nat. UJEP Brunensis, Arch. Math. VII (1971), 65–76. (1971) Zbl0241.34037MR0306610
  5. Third Order Linear Differential Equations, D. Reidel Publ. Co., Dordrecht, 1987. (1987) MR0882545
  6. Ordinary Differential Equations, J. Wiley and Sons, New York, 1964. (1964) Zbl0125.32102MR0171038
  7. Asymptotical Properties of Solutions of Nonautonomous Ordinary Differential Equations, Nauka, Moscow, 1990. (Russian) (1990) 
  8. Approximate Solution of Operator Equations, Nauka, Moscow, 1969. (Russian) (1969) MR0259635
  9. Global Properties of Linear Ordinary Differential Equations, Academia, Praha, 1991. (1991) Zbl0784.34009MR1192133
  10. Foundations of Differential Inequalities, Pan. Wydav. Nauk., Warsaw, 1976. (Polish) (1976) MR0457827
  11. 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. (1978) MR0534812
  12. Existence of a Monotone Solution of a Nonlinear Differential Equation, J. Math. Anal. Appl. 192 (1995), 1–15. (1995) MR1329409
  13. On a Class of Linear n -th Order Differential Equations, Czech. Math. J. 39(114) (1989), 350–369. (1989) 

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