Existence of positive solutions of n -dimensional system of nonlinear differential equations entering into a singular point

Josef Diblík; Miroslava Růžičková

Archivum Mathematicum (2000)

  • Volume: 036, Issue: 5, page 435-446
  • ISSN: 0044-8753

How to cite

top

Diblík, Josef, and Růžičková, Miroslava. "Existence of positive solutions of $n$-dimensional system of nonlinear differential equations entering into a singular point." Archivum Mathematicum 036.5 (2000): 435-446. <http://eudml.org/doc/248569>.

@article{Diblík2000,
author = {Diblík, Josef, Růžičková, Miroslava},
journal = {Archivum Mathematicum},
keywords = {singular problem; positive solution; implicit function},
language = {eng},
number = {5},
pages = {435-446},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Existence of positive solutions of $n$-dimensional system of nonlinear differential equations entering into a singular point},
url = {http://eudml.org/doc/248569},
volume = {036},
year = {2000},
}

TY - JOUR
AU - Diblík, Josef
AU - Růžičková, Miroslava
TI - Existence of positive solutions of $n$-dimensional system of nonlinear differential equations entering into a singular point
JO - Archivum Mathematicum
PY - 2000
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 036
IS - 5
SP - 435
EP - 446
LA - eng
KW - singular problem; positive solution; implicit function
UR - http://eudml.org/doc/248569
ER -

References

top
  1. 1. K. Balla, On solution of singular boundary problems for nonlinear systems of ordinary differential equations, Zh. vych. mat. i mat. fiz., 20 (1980), 909–922 (in Russian). (1980) MR0585288
  2. 2. J. Baštinec, J. Diblík, Three–point singular boundary-value problem for a system of three differential equations, Math. Communication, 3 (1998), 211–219. (1998) MR1679740
  3. 3. J. Diblík, On existence of O-curves of a singular system of differential equations, Math. Nachr., 122 (1985), 247–258 (in Russian). (1985) MR0871207
  4. 4. J. Diblík, On existence of solutions of a real system of ordinary differential equations, entering into a singular point, Ukrainian Math. J., 38 (1986), 701–706 (in Russian). (1986) MR0881960
  5. 5. J. Diblík, On existence of O - curves of systems of ordinary differential equations, that are asymptotically equal to a given curve, Differential Equations, 23 (1987), 2159 – 2161 (in Russian). (1987) 
  6. 6. J. Diblík, Some asymptotic properties of solutions of certain classes of ordinary differential equations, J. Math. Anal. Appl., 165 (1992), 288–304. (1992) MR1151073
  7. 7. J. Diblík, On asymptotic behaviour of solutions of certain classes of ordinary differential equations, J. Diff. Equat., 95 (No 2), 203–217, 1992. (1992) MR1165420
  8. 8. J. Diblík, M. Růžičková, Existence of solutions of a nonlinear differential system of differential equations entering into a singular point, Studies of University in Žilina, Math. – Phys. Ser. 32 (1999), 11–19. (1999) MR1755619
  9. 9. Ph. Hartman, Ordinary differential equations, Second Edition, Birkhäuser, 1982. (1982) MR0658490
  10. 10. V.A. Chechyk, Investigations of systems ordinary differential equations with singularities, Trudy Moskovsk. Mat. Obsc., 8 (1959), 155–198 (in Russian). (1959) MR0107066
  11. 11. I.T. Kiguradze, Some singular boundary value problems for ordinary differential equations, Izd. Tbilisskovo univ., Tbilisi, 1975, 352 pp. (in Russian). (1975) MR0499402
  12. 12. N.B. Konyukhova, Singular Cauchy problems for systems of ordinary differential equations, Zh. vych. mat. i mat. fiz., 23 (1983), 629–645 (in Russian). (1983) Zbl0555.34002MR0706888
  13. 13. Chr. Nowak, Some remarks on a paper by Samimi on nonuniqueness criteria for ordinary differential equations, Appl. Anal., 47 (1992), 39–44. (1992) Zbl0792.34002MR1214647
  14. 14. D. O’Regan, Nonresonant nonlinear singular problems in the limit circle case, J. Math. Anal. Appl., 197 (1996), 708–725. (197) MR1373074
  15. 15. M. Růžičková, The asymptotic properties of solutions of differential system of the form g i ( x ) y i ' = u i ( y i ) + f i ( x , y 1 , . . . , y n ) , i = 1 , 2 , . . . , n in some neighbourhood of a singular point, Acta Univ. Palack. Olomuc. Fac. Rer. Nat., Math. 32 (1993), 151–158. (1993) 
  16. 16. T. Ważewski, Sur un principe topologique de l’examen de l’ allure asymptotique des intégrales des équations différentielles ordinaires, Ann. de la Soc. Polon. de Mathèmatique, 20 (1947), (Krakow 1948), 279–313. (1947) MR0026206

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.