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Some existence theorems for differential inclusions in Hilbert spaces

Published online by Cambridge University Press:  17 April 2009

Shih-Sen Chang ,
Yu-Qing Chen  and
Byung Soo Lee
Yu-Qing Chen
Affiliation:
Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, People's Republic of China
Byung Soo Lee
Affiliation:
Department of Mathematics, Kyungsung University, Pusan 608-736, Korea
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Abstract

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Some existence theorem for solutions of two kinds of differential inclusions with monotone type mappings in Hilbert spaces are given.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 54 , Issue 2 , October 1996 , pp. 317 - 327
Copyright
Copyright © Australian Mathematical Society 1996

References

REFERENCES

[1]Aubin, J.P. and Celina, A., Differential inclusions (Springer-Verlag, New York, Heidelberg, Berlin, 1984).CrossRefGoogle Scholar
[2]Attouch, H. and Dalamaian, D., ‘On multivalued evolution equations in Hilbert spaces’, Israel J. Math. 12 (1972), 273–390.CrossRefGoogle Scholar
[3]Barbu, V., Nonlinear semigroups and differential equations in Banach spaces (Noord-Horff, 1976).CrossRefGoogle Scholar
[4]Brezis, H., Operateurs maximaux monotones et semigroupes de Hilbert (North-Holland, 1973).Google Scholar
[5]Browder, F.E., ‘Existence of periodic solutions for nonlinear equations of evolution’, Proc. Nat. Acad. Sci. U.S.A. 6 (1965), 1272–1276.CrossRefGoogle Scholar
[6]Browder, F.E., ‘Nonlinear operators and nonlinear equations of evolution in Banach spaces’, in Proc. Sympos. Pure Math. 18 (American Mathematical Society, Providence, RI, 1976), pp. 1–308.Google Scholar
[7]Cellina, A. and Marchi, M.V., ‘Nonconvex perturbations of mamimal monotone differential inclusions‘, Israel J. Math. 46 (1983), 1–11.CrossRefGoogle Scholar
[8]Cellina, A. and Staicu, V., ‘On evolution equations having monotonicities of opposite sign’, J. Differential Equations 90 (1991), 71–80.CrossRefGoogle Scholar
[9]Deimling, K., Ordinary differential equations in Banach spaces, Lecture Notes in Mathematics 596 (Springer-Verlag, NewYork, Heidelberg, Berlin, 1977).CrossRefGoogle Scholar
[10]Golombo, G., Fonda, A. and Ornelas, A., ‘A nonconvex semi-continuous perturbation of maximal monotone differential inclusions’, Israel J. Math 61 (1988), 211–218.CrossRefGoogle Scholar
[11]Kato, T., ‘Nonlinear semigroups and evolution equations’, J. Math. Soc. Japan 19 (1976), 508–520.Google Scholar
[12]Kravritis, D. and Papageorgiou, N.S., ‘Multivalued perturbations of subdifferential type evolution equations in Hilbert spaces’, J. Differential Equations 76 (1988), 238–255.CrossRefGoogle Scholar
[13]Lakshmikantham, V. and Leela, S., Nonlinear differential equations in abstract spaces (Pergamon Press, New York, 1981).Google Scholar
[14]Mitidieri, E. and Vrabie, I.I., ‘Differential inclusions governed by non-convex perturbations of m-accretive operators’, Differential Integral Equations 2 (1989), 525–531.CrossRefGoogle Scholar
[15]Milojevic, P.S. and Petryshyn, W.V., ‘Continuation theorems and the approximation solvability of equations involving multivalued A-proper mappings’, J. Math. Anal. Appl. 60 (1977), 658–697.CrossRefGoogle Scholar
[16]Petryshyn, W.V., ‘Antipodes theorems for A-proper mappings of the modified type (S +) or (S +) and to mappings with the Pm property’, J. Fund. Anal. 71 (1971), 165–211.CrossRefGoogle Scholar
[17]Pascali, D. and Sburlan, S., Nonlinear mappings of monotone type (Sijthoff and Noordhoff International Publishers, Romania, 1978).CrossRefGoogle Scholar