Multiple bounded solutions of differential inclusions: The Nielsen theory approach

Journal of Differential Equations

Volumn 155, Issue 2, 1999, Pages 285-310

  Andres, Jan ^a  

^a PALACKÝ UNIVERSITY   (Czech Republic)

Author keywords

Nielsen number; u.s.c. maps with R values; ANRs; Fr chet spaces; Carath odory differential inclusions and equations; multiplicity results

Indexed keywords

EID: 0033164817     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1006/jdeq.1998.3582     Document Type: Article

References (35)

1. Andres J. A target problem for differential inclusions with state-space constraints. Demonstratio Math. 30:1997;783-790.
2. J. Andres, Almost periodic and bounded solutions of Carathéodory differential inclusions, Differential Integral Equations, in press.
3. J. Andres, G. Gabor, and, G. Górniewicz, Boundary value problems on infinite intervals, Trans. Amer. Math. Soc, in press.
4. J. Andres, L. Górniewicz, and, J. Jezierski, A generalized Nielsen number and multiplicity results for differential inclusions, Topology Appl, in press.
5. Aubin J.-P., Cellina A. Differential Inclusions. 1982;Springer-Verlag, Berlin.
6. Bader R. A sufficient condition for the existence of multiple periodic solutions of differential inclusions. Geba K., Górniewicz L. Topology in Nonlinear Analysis. Banach Center Publ. 35:1996;129-138 PWN, Warsaw.
7. Bader R., Kryszewski W. Fixed point index for compositions of set-valued maps with the proximally ∞-connected values on arbitrary ANR's. Set-Valued Anal. 2:1994;459-480.
8. Jiang Boju. Nielsen Fixed Point Theory. Contemp. Math. 14:1983;Amer. Math. Soc. Providence.
9. Borsuk K. Theory of Retracts. 1967;PWN, Warsaw.
10. Borisovich A. Yu., Kucharski Z., Marzantowicz W. Nielsen numbers and lower estimates for the number of solutions to a certain system of nonlinear integral equations. Appl. Aspects of Global Analysis. New Developments in Global Analysis Series. 1994;Voronezh Univ. Press. p. 3-10.
11. Brooks R. B. S., Brown R. F., Pak J., Taylor D. H. Nielsen numbers of maps of tori. Proc. Amer. Math. Soc. 52:1975;398-400.
12. Brown R. F. The Lefschetz Fixed Point Theorem. 1971;Scott, Foresman, Glenview.
13. Brown R. F. Multiple solutions to parametrized nonlinear differential systems from Nielsen fixed point theory. Rassias Th. M. Nonlinear Analysis. 1987;89-98 World Scientific, Singapore.
14. Brown R. F. Topological identification of multiple solutions to parametrized nonlinear equations. Pacific J. Math. 131:1988;51-69.
15. Brown R. F. Nielsen fixed point theory and parametrized differential equations. Contemp. Math. 1988;Amer. Math. Soc. Providence. p. 33-45.
16. Brown R. F., Zezza P. Multiple local solutions to nonlinear control processes. J. Optim. Theory Appl. 67:1990;463-485.
17. Dzedzej Z. Fixed point index theory for a class of nonacyclic multivalued maps. Dissertationes Math. 253:1985;1-58.
18. Fečkan M. Nielsen fixed point theory and nonlinear equations. J. Differential Equations. 106:1993;312-331.
19. Fečkan M. Multiple perturbed solutions near nondegenerate manifolds of solutions. Comment. Math. Univ. Carolin. 34:1993;635-643.
20. Fečkan M. Multiple periodic solutions of small vector fields on differentiable manifolds. J. Differential Equations. 113:1994;189-200.
21. Górniewicz L., Granas A., Kryszewski W. On the homotopy method in the fixed point index theory of multi-valued mappings of compact absolute neighbourhood retracts. J. Math. Anal. Appl. 161:1991;457-473.
22. Górniewicz L. Homological method in fixed-point theory of multivalued maps. Dissertationes Math. 129:1976;1-71.
23. Granas A. The Leray-Schauder index and the fixed point theory for arbitrary ANRs. Bull. Soc. Math. France. 100:1972;209-228.
24. Jezierski J. The Nielsen relation for multivalued maps. SERDICA. 13:1987;174-181.
25. Jarník J., Kurzweil J. Integral of multivalued mappings and its connection with differential relations. Cas. Pěst. Mat. 108:1983;8-28.
26. Tsai-han Kiang. The Theory of Fixed Point Classes. 1989;Springer-Verlag, Berlin.
27. Krasnosel'skii M. A. The Operator of Translation along the Trajectories of Differential Equations. Transl. Math. Monogr. 19:1968;Amer. Math. Soc. Providence.
28. Kryszewski W., Miklaszewski D. The Nielsen number of set-valued maps: An Approximation approach. SERDICA. 15:1989;336-344.
29. McCord C. K. Nielsen Theory and Dynamical Systems. Contemp. Math. 152:1993;Amer. Math. Soc. Providence.
30. Musielak J. Introduction to Functional Analysis. 1976;PWN, Warsaw.
31. Rybinski L. On Carathéodory type selectors. Fund. Math. 125:1985;187-193.
32. Schirmer H. A Nielsen number for fixed points and near points of small multifunctions. Fund. Math. 88:1975;145-156.
33. H. Schirmer, An index and a Nielsen number for n-valued multifunctions, Fund. Math.1241984, 207-219.
34. Scholz K. The Nielsen fixed point theory for non-compact spaces. Rocky Mountain J. Math. 4:1974;81-87.
35. Spanier E. Algebraic Topology. 1966;McGraw-Hill, New York.