On quadratically integrable solutions of the second order linear equation

T. Chantladze; Nodar Kandelaki; Alexander Lomtatidze

Archivum Mathematicum (2001)

  • Volume: 037, Issue: 1, page 57-62
  • ISSN: 0044-8753

Abstract

top
Integral criteria are established for dim V i ( p ) = 0 and dim V i ( p ) = 1 , i ∈ { 0 , 1 } , where V i ( p ) is the space of solutions u of the equation u ' ' + p ( t ) u = 0 satisfying the condition ∫ + ∞ u 2 ( s ) s i d s < + ∞ .

How to cite

top

Chantladze, T., Kandelaki, Nodar, and Lomtatidze, Alexander. "On quadratically integrable solutions of the second order linear equation." Archivum Mathematicum 037.1 (2001): 57-62. <http://eudml.org/doc/248743>.

@article{Chantladze2001,
abstract = {Integral criteria are established for $\dim V_i(p)=0$ and $\dim V_i(p)=1, i\in \lbrace 0,1\rbrace $, where $V_i(p)$ is the space of solutions $u$ of the equation \[ u^\{\prime \prime \}+p(t)u=0 \] satisfying the condition \[ \int ^\{+\infty \}\frac\{u^2(s)\}\{s^i\}ds<+\infty \,. \]},
author = {Chantladze, T., Kandelaki, Nodar, Lomtatidze, Alexander},
journal = {Archivum Mathematicum},
keywords = {second order linear equation; quadratically integrable solutions; vanishing at infinity solutions; second order linear equation; quadratically integrable solutions; vanishing at infinity solutions},
language = {eng},
number = {1},
pages = {57-62},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {On quadratically integrable solutions of the second order linear equation},
url = {http://eudml.org/doc/248743},
volume = {037},
year = {2001},
}

TY - JOUR
AU - Chantladze, T.
AU - Kandelaki, Nodar
AU - Lomtatidze, Alexander
TI - On quadratically integrable solutions of the second order linear equation
JO - Archivum Mathematicum
PY - 2001
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 037
IS - 1
SP - 57
EP - 62
AB - Integral criteria are established for $\dim V_i(p)=0$ and $\dim V_i(p)=1, i\in \lbrace 0,1\rbrace $, where $V_i(p)$ is the space of solutions $u$ of the equation \[ u^{\prime \prime }+p(t)u=0 \] satisfying the condition \[ \int ^{+\infty }\frac{u^2(s)}{s^i}ds<+\infty \,. \]
LA - eng
KW - second order linear equation; quadratically integrable solutions; vanishing at infinity solutions; second order linear equation; quadratically integrable solutions; vanishing at infinity solutions
UR - http://eudml.org/doc/248743
ER -

References

top
  1. Wintner A., On the non-existence of conjugate points, Amer. J. Math. 73 (1951), 368–380. (1951) MR0042005
  2. Kneser A., Untersuchung und asymptotische Darstellung der Integrale gewisser Differentialgleichungen bei grossen reelen Werten des Arguments, J. Reine Angew. Math. 116 (1896), 178–212. 
  3. Kiguradze I.T., Chanturia T.A., Asymptotic properties of solutions of nanautonomous ordinary differential equations, Kluwer Academic Publishers, Dordrecht–Boston–London, 1992. (1992) 
  4. Kiguradze I.T., Shekhter B.L., Singular boundary value problems for second order differential equations, in “Current Problems in Mathematics: Newest Results,” vol. 30, pp. 105–201, Itogi Nauki i Tekhniki, Akad. Nauk SSSR, Vsesoyzn. Inst. Nauchn. i Tekhn. Inform., Moscow, 1987. (1987) MR0925830
  5. Chantladze T., Kandelaki N., Lomtatidze A., Oscillation and nonoscillation criteria for second order linear equations, Georgian Math. J. 6 (1999), No 5, 401–414. (1999) MR1692963

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.