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Keywords:
boundary value problems; multivalued differential equations; topological transversality theorem; fixed points; differential inequalities
boundary value problems; multivalued differential equations; topological transversality theorem; fixed points; differential inequalities
Summary:
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.
References:
[1] Agarwal R. P., O’Regan D.: Set valued mappings With applications in nonlinear analysis. Taylor & Francis, London 2002. MR 1938034 | Zbl 0996.00018
[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. MR 1800619 | Zbl 0996.34012
[3] Andres J., Bader R.: Asymptotic boundary value problems in Banach spaces. J. Math. Anal. Appl. 274 (2002), 437–457. MR 1936707 | Zbl 1025.34059
[4] Anichini G.: Boundary value problems for multivalued differential equations and controllability. J. Math. Anal. Appl. 105 (1985), 372–382. MR 0778472
[5] Anichini G., Conti G.: Boundary value problems for systems of differential equations. Nonlinearity 1 (1988), 1–10.
[6] Aubin J. P., Cellina A.: Differential inclusions, Set-valued maps and viability theory. Springer Verlag, New York 1984. MR 0755330 | Zbl 0538.34007
[7] Bernfeld S., Lakshmikantham V.: An introduction to nonlinear boundary value Problems. Academic Press, New York 1974. MR 0445048 | Zbl 0286.34018
[8] Deimling K.: Multivalued differential equations. W. de Gruyter, Berlin 1992. MR 1189795 | Zbl 0820.34009
[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. MR 1170147 | Zbl 0820.34009
[10] Frigon M.: Application de la transversalite topologique a des problemes non lineaires pour des equations differentielles ordinaires. Dissertationes Math. 296, PWN, Warsaw 1990. MR 1075674
[11] Granas A., Dugundji J.: Fixed point theory. Springer Verlag 2003. MR 1987179 | Zbl 1025.47002
[12] Granas A., Frigon M.: Topological methods in differential equations and inclusions. Kluwer Academic Publ., Dordrecht 1995. MR 1368668 | Zbl 0829.00024
[13] Hu S., Papageorgiou N. S.: Handbook of multivalued analysis. 2 Applications, Kluwer Acad. Publ. Dordrecht 2000. MR 1741926 | Zbl 0943.47037
[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. MR 0196178 | Zbl 0151.10703
[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. MR 1475574 | Zbl 0893.26006
[16] Miller L. E.: Generalized boundary value problems. J. Math. Anal. Appl. 74 (1980), 233–246. MR 0568383 | Zbl 0431.34022
[17] O’Regan D.: Fixed-point theory for the sum of two operators. Applied Math. Letters 9 1 (1996), 1–8. Zbl 0858.34049
[18] Pruzko T.: Topological degree methods in multivalued boundary value problems. Nonlinear Anal. T. M. A. 5 9 (1982), 959–973. MR 0633011
[19] Senkyrík M., Guenther R.: Boundary value problems with discontinuities in the spacial variable. J. Math. Anal. Appl. 193 (1995), 296–305. MR 1338514
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