Rocky Mountain Journal of Mathematics

Existence of Positive Solutions of a Singular Initial Problem for a Nonlinear System of Differential Equations

Josef Diblík and Miroslava Rğzǐčková

Full-text: Open access

Article information

Source
Rocky Mountain J. Math., Volume 34, Number 3 (2004), 923-944.

Dates
First available in Project Euclid: 5 June 2007

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1181069835

Digital Object Identifier
doi:10.1216/rmjm/1181069835

Mathematical Reviews number (MathSciNet)
MR2087439

Zentralblatt MATH identifier
1080.34001

Citation

Diblík, Josef; Rğzǐčková, Miroslava. Existence of Positive Solutions of a Singular Initial Problem for a Nonlinear System of Differential Equations. Rocky Mountain J. Math. 34 (2004), no. 3, 923--944. doi:10.1216/rmjm/1181069835. https://projecteuclid.org/euclid.rmjm/1181069835


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References

  • K. Balla, Solution of singular boundary value problems for non-linear systems of ordinary differential equations, USSR Comput. Math. Math. Phys. 20 (1980), 100-115.
  • Ch. Conley, Isolated invariant sets and the Morse index, Regional Conf. Ser. in Math., Amer. Math. Soc., Providence, 1978.
  • J. Diblík, Some asymptotic properties of solutions of certain classes of ordinary differential equations, J. Math. Anal. Appl. 165 (1992), 288-304.
  • --------, On asymptotic behaviour of solutions of certain classes of ordinary differential equations, J. Differential Equations 95 (1992), 203-217.
  • Ph. Hartman, Ordinary differential equations, Second edition, Birkhäuser, Berlin, 1982.
  • V.A. Chechyk, Investigations of systems ordinary differential equations with singularities, Trudy Moskovsk. Mat. Obsc. 8 (1959), 155-198 (in Russian).
  • A.F. Izé, Asymptotic behavior of solutions of a class of differential equations in infinite-dimensional spaces, Nonlinear Anal., Theory, Methods Appl. 39 (2000), 289-303.
  • I.T. Kiguradze, Some singular boundary value problems for ordinary differential equations, Izd. Tbilisskovo Univ., Tbilisi, 1975 (in Russian).
  • N.B. Konyukhova, Singular Cauchy problems for systems of ordinary differential equations, USSR Comput. Math. Math. Phys. 23 (1983), 72-82.
  • Chr. Nowak, Some remarks on a paper by Samimi on nonuniqueness criteria for ordinary differential equations, Appl. Anal. 47 (1992), 39-44.
  • D. O'Regan, Nonresonant nonlinear singular problems in the limit circle case, J. Math. Anal. Appl. 197 (1996), 708-725.
  • J. Smoller, Shock waves and reaction-diffusion equations, Springer-Verlag, Berlin, 1983.
  • R. Srzednicki, On the structure of the Conley index, in Equadiff $99$, Internat. Conf. on Differential Equations (Berlin 1999), Vol. 1 (2000), 231-240.
  • --------, On periodic solutions inside isolating chains, J. Differential Equations 165 (2000), 42-60.
  • --------, Periodic and bounded solutions in blocks for time-periodic nonautonomous ordinary differential equations, Nonlinear. Anal., Theory, Methods Appl. 22 (1994), 707-737.
  • T. Wa $\dotz$ewski, 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.
  • F.W. Wilson and J.A. Yorke, Liapunov functions and isolating blocks, J. Differential Equations 13 (1973), 106-123.