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Periodic solutions for nonconvex differential inclusions
Author(s):
Shouchuan
Hu;
Dimitrios
A.
Kandilakis;
Nikolaos
S.
Papageorgiou
Journal:
Proc. Amer. Math. Soc.
127
(1999),
89-94.
MSC (1991):
Primary 34C25, 34A60
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Abstract:
In this paper we prove the existence of periodic solutions for differential inclusions with nonconvex-valued orientor field. Our proof is based on degree theoretic arguments.
References:
- 1.
- J. P. Aubin and A. Cellina, Differential Inclusions, Springer-Verlag, Berlin, 1984. MR 85j:49010
- 2.
- A. Bressan and G. Colombo, Extensions and selections of maps with decomposable values, Studia Math. 90 (1988), 69-86. MR 89j:54021
- 3.
- H. Brezis, Analyse Fonctionelle, Masson, Paris, 1983. MR 85a:46001
- 4.
- G. Haddad and J.-M. Lasry, Periodic solutions of functional-differential inclusions and fixed points of
-selectionable correspondences, J. Math. Anal. Appl. 96 (1983), 295-312. MR 84m:34015 - 5.
- E. Hille and R. Phillips, Functional Analysis and Semigroups, AMS Colloq. Publ., Vol. 31, Amer. Math. Soc., Providence, RI, 1957. MR 54:11077
- 6.
- S. Hu and N. S. Papageorgiou, On the existence of periodic solutions for nonconvex valued differential inclusions in
, Proc. Amer. Math. Soc. 123 (1995), 3043-3050. MR 95m:34030 - 7.
- J. Macki, P. Nistri, and P. Zecca, The existence of periodic solutions to nonautonomous differential inclusions, Proc. Amer. Math. Soc. 104 (1988), 840-844. MR 89e:34027
- 8.
- J. Mawhin, Topological Degree Methods in Nonlinear Boundary Value Problems, CBMS, Regional Conference Series in Math., Vol. 40, Amer. Math. Soc., Providence, RI, 1979. MR 80c:47055
- 9.
- N. S. Papageorgiou, On infinite dimensional control systems with state and control constraints, Proc. Indian Acad. Sci. 100 (1990), 65-77. MR 91e:49018
- 10.
- N. S. Papageorgiou, On Fatou's lemma and parametric integrals for set valued functions, J. Math. Anal. Appl. 187 (1994), 809-825. MR 95m:28012
- 11.
- S. Plaskacz, Periodic solutions of differential inclusions on compact subsets of
, J. Math. Anal. Appl. 148 (1990), 202-212. MR 91d:34017 - 12.
- D. Wagner, Survey on measurable selection theorems, SIAM J. Control Optim. 15 (1977), 859-903. MR 58:6137
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Additional Information:
Shouchuan
Hu
Affiliation:
Department of Mathematics, Southwest Missouri State University, Springfield, Missouri 65804
Email:
hu@math.smsu.edu
Dimitrios
A.
Kandilakis
Affiliation:
Department of Mathematics, University of the Aegean, 83200 Karlovassi, Samos, Greece
Nikolaos
S.
Papageorgiou
Affiliation:
Department of Mathematics, National Technical University, Zografou Campus, Athens 15780, Greece
Email:
npapg@math.ntua.gr
DOI:
10.1090/S0002-9939-99-04338-5
PII:
S 0002-9939(99)04338-5
Keywords:
Lower semicontinuous multifunction,
measurable multifunction,
continuous selector,
a priori bound,
compact embedding,
Leray-Schauder degree,
compact homotopy,
homotopy invariance
Received by editor(s):
September 23, 1996
Additional Notes:
The second author's research was supported by Grant PENED 678(94)
Communicated by:
Hal L. Smith
Copyright of article:
Copyright
1999,
American Mathematical Society
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