Two-points boundary value problems for Carathéodory second order equations

Valentina Taddei

Archivum Mathematicum (2008)

  • Volume: 044, Issue: 2, page 93-103
  • ISSN: 0044-8753

Abstract

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Using a suitable version of Mawhin’s continuation principle, we obtain an existence result for the Floquet boundary value problem for second order Carathéodory differential equations by means of strictly localized C 2 bounding functions.

How to cite

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Taddei, Valentina. "Two-points boundary value problems for Carathéodory second order equations." Archivum Mathematicum 044.2 (2008): 93-103. <http://eudml.org/doc/250435>.

@article{Taddei2008,
abstract = {Using a suitable version of Mawhin’s continuation principle, we obtain an existence result for the Floquet boundary value problem for second order Carathéodory differential equations by means of strictly localized $ C^2 $ bounding functions.},
author = {Taddei, Valentina},
journal = {Archivum Mathematicum},
keywords = {continuation principle; coincidence degree; second order differential systems; bound sets; Floquet type boundary conditions; continuation principle; coincidence degree; second order differential system; bound set; Floquet type boundary condition},
language = {eng},
number = {2},
pages = {93-103},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Two-points boundary value problems for Carathéodory second order equations},
url = {http://eudml.org/doc/250435},
volume = {044},
year = {2008},
}

TY - JOUR
AU - Taddei, Valentina
TI - Two-points boundary value problems for Carathéodory second order equations
JO - Archivum Mathematicum
PY - 2008
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 044
IS - 2
SP - 93
EP - 103
AB - Using a suitable version of Mawhin’s continuation principle, we obtain an existence result for the Floquet boundary value problem for second order Carathéodory differential equations by means of strictly localized $ C^2 $ bounding functions.
LA - eng
KW - continuation principle; coincidence degree; second order differential systems; bound sets; Floquet type boundary conditions; continuation principle; coincidence degree; second order differential system; bound set; Floquet type boundary condition
UR - http://eudml.org/doc/250435
ER -

References

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  1. Andres, J., Malaguti, L., Taddei, V., 10.1155/S108533750321006X, Abstr. Appl. Anal. 9 (2003), 547–571. (2003) Zbl1036.34011MR1981485DOI10.1155/S108533750321006X
  2. Andres, J., Malaguti, L., Taddei, V., A bounding function approach to multivalued boundary values problems, Set-valued Methods in Dynamic Systems, Special Issue of Dynam. Systems Appl. 16 (2007), 37–48. (2007) MR2305427
  3. Erbe, L., Palamides, P. K., 10.1016/0022-247X(87)90141-7, J. Math. Anal. Appl. 127 (1) (1987), 80–92. (1987) Zbl0635.34017MR0904211DOI10.1016/0022-247X(87)90141-7
  4. Erbe, L., Schmitt, K., Boundary value problems for second order differential equations, Nonlinear Anal. Appl., Proc. 7th Int. Conf. (Arlington 1986), Lect. Notes Pure Appl. Math. 109 (1987), 179–184. (1987) Zbl0636.34012MR0912292
  5. Gaines, R .E., Mawhin, J., Coincidence degree and nonlinear differential equations, Lectures Notes in Math., Springer–Verlag, Berlin 586 (1977). (1977) Zbl0339.47031MR0637067
  6. Hartman, P., Ordinary Differential Equations, Wiley-Interscience, New York, 1969. (1969) MR0419901
  7. Lloyd, N. G., Degree Theory, Cambridge University Press, Cambridge, 1978. (1978) Zbl0367.47001MR0493564
  8. Mawhin, J., 10.1016/0022-0396(74)90013-8, J. Differential Equations 16 (1974), 257–269. (1974) Zbl0301.34019MR0361250DOI10.1016/0022-0396(74)90013-8
  9. Mawhin, J., The Bernstein-Nagumo problem and two-point boundary value problem for ordinary differential equations, Qualitative theory of differential equations, Colloq. Math. Soc. János Bolyai, Szeged 30 II (1979), 709–740. (1979) MR0680616
  10. Mawhin, J., Topological Degree Methods in Nonlinear Boundary Value Problems, CBMS Series, Amer. Math. Soc., Providence, RI 40 (1979). (1979) Zbl0414.34025MR0525202
  11. Mawhin, J., Thompson, H. B., 10.1023/B:JODY.0000009739.00640.44, J. Dynam. Differential Equations 15 (2-3) (2003), 327–334. (2003) Zbl1055.34035MR2046722DOI10.1023/B:JODY.0000009739.00640.44
  12. Mawhin, J., Ward Jr., J. R., Guiding-like functions for periodic or bounded solutions of ordinary differential equations, Discrete Contin. Dynam. Systems 8 (1) (2002), 39–54. (2002) Zbl1087.34518MR1877827
  13. Scorza Dragoni, G., Intorno a un criterio di esistenza per un problema di valori ai limiti, Rend. Accad. Naz. Lincei 28 (6) (1938), 317–325. (1938) 
  14. Taddei, V., Zanolin, F., Bound sets and two-points boundary value problems for second order differential equations, Georg. Math. J., Special issue dedicated to 70th birthday of Prof. I. Kiguradze 14 (2) (2007). (2007) MR2341286
  15. Thompson, H. B., 10.1007/BF02844736, Rend. Circ. Mat. Palermo (2) 35 (2) (1986), 261–275. (1986) Zbl0608.34018MR0892085DOI10.1007/BF02844736

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