Boundary value problems for first order multivalued differential systems

Abdelkader Boucherif; N.Chiboub-Fellah Merabet

Archivum Mathematicum (2005)

  • Volume: 041, Issue: 2, page 187-195
  • ISSN: 0044-8753

Abstract

top
We present some existence results for boundary value problems for first order multivalued differential systems. Our approach is based on topological transversality arguments, fixed point theorems and differential inequalities.

How to cite

top

Boucherif, Abdelkader, and Merabet, N.Chiboub-Fellah. "Boundary value problems for first order multivalued differential systems." Archivum Mathematicum 041.2 (2005): 187-195. <http://eudml.org/doc/249504>.

@article{Boucherif2005,
abstract = {We present some existence results for boundary value problems for first order multivalued differential systems. Our approach is based on topological transversality arguments, fixed point theorems and differential inequalities.},
author = {Boucherif, Abdelkader, Merabet, N.Chiboub-Fellah},
journal = {Archivum Mathematicum},
keywords = {boundary value problems; multivalued differential equations; topological transversality theorem; fixed points; differential inequalities; multivalued differential equations; topological transversality theorem},
language = {eng},
number = {2},
pages = {187-195},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Boundary value problems for first order multivalued differential systems},
url = {http://eudml.org/doc/249504},
volume = {041},
year = {2005},
}

TY - JOUR
AU - Boucherif, Abdelkader
AU - Merabet, N.Chiboub-Fellah
TI - Boundary value problems for first order multivalued differential systems
JO - Archivum Mathematicum
PY - 2005
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 041
IS - 2
SP - 187
EP - 195
AB - We present some existence results for boundary value problems for first order multivalued differential systems. Our approach is based on topological transversality arguments, fixed point theorems and differential inequalities.
LA - eng
KW - boundary value problems; multivalued differential equations; topological transversality theorem; fixed points; differential inequalities; multivalued differential equations; topological transversality theorem
UR - http://eudml.org/doc/249504
ER -

References

top
  1. Agarwal R. P., O’Regan D., Set valued mappings With applications in nonlinear analysis, Taylor & Francis, London 2002. Zbl0996.00018MR1938034
  2. Andres J., Nielsen number and multiplicity results for multivalued boundary value problems, Boston MA, Birkhäuser, Progr. Nonlinear Differ. Equ. Appl. 43 (2001), 175–187. Zbl0996.34012MR1800619
  3. Andres J., Bader R., Asymptotic boundary value problems in Banach spaces, J. Math. Anal. Appl. 274 (2002), 437–457. Zbl1025.34059MR1936707
  4. Anichini G., Boundary value problems for multivalued differential equations and controllability, J. Math. Anal. Appl. 105 (1985), 372–382. (1985) MR0778472
  5. Anichini G., Conti G., Boundary value problems for systems of differential equations, Nonlinearity 1 (1988), 1–10. (1988) 
  6. Aubin J. P., Cellina A., Differential inclusions, Set-valued maps and viability theory, Springer Verlag, New York 1984. (1984) Zbl0538.34007MR0755330
  7. Bernfeld S., Lakshmikantham V., An introduction to nonlinear boundary value Problems, Academic Press, New York 1974. (1974) Zbl0286.34018MR0445048
  8. Deimling K., Multivalued differential equations, W. de Gruyter, Berlin 1992. (1992) Zbl0820.34009MR1189795
  9. Deimling K., Multivalued differential equations and dry friction problems, in Delay and Differential Equations, (A. M. Fink, R. K. Miller and W. Kliemann, Eds.), 99–106, World Scientific Publ.,N. J. 1992. (1992) Zbl0820.34009MR1170147
  10. Frigon M., Application de la transversalite topologique a des problemes non lineaires pour des equations differentielles ordinaires, Dissertationes Math. 296, PWN, Warsaw 1990. (1990) MR1075674
  11. Granas A., Dugundji J., Fixed point theory, Springer Verlag 2003. Zbl1025.47002MR1987179
  12. Granas A., Frigon M., Topological methods in differential equations and inclusions, Kluwer Academic Publ., Dordrecht 1995. (1995) Zbl0829.00024MR1368668
  13. Hu S., Papageorgiou N. S., Handbook of multivalued analysis, 2 Applications, Kluwer Acad. Publ. Dordrecht 2000. Zbl0943.47037MR1741926
  14. Lasota A., Opial Z., An application of the Kakutani-Ky-Fan theorem in the theory of ordinary differential equations, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 13 (1965), 781–786. (1965) Zbl0151.10703MR0196178
  15. Medved M., A new approach to an analysis of Henry type integral inequalities and their Bihari type versions, J. Math. Anal. Appl. 214 (1997), 349–366. (1997) Zbl0893.26006MR1475574
  16. Miller L. E., Generalized boundary value problems, J. Math. Anal. Appl. 74 (1980), 233–246. (1980) Zbl0431.34022MR0568383
  17. O’Regan D., Fixed-point theory for the sum of two operators, Applied Math. Letters 9 1 (1996), 1–8. (1996) Zbl0858.34049
  18. Pruzko T., Topological degree methods in multivalued boundary value problems, Nonlinear Anal. T. M. A. 5 9 (1982), 959–973. (1982) MR0633011
  19. Senkyrík M., Guenther R., Boundary value problems with discontinuities in the spacial variable, J. Math. Anal. Appl. 193 (1995), 296–305. (193) MR1338514

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.