Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-01T20:05:14.601Z Has data issue: false hasContentIssue false

Some existence theorems for differential inclusions in Hilbert spaces

Published online by Cambridge University Press:  17 April 2009

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
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

Type
Research Article
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), 273390.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), 12721276.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. 1308.Google Scholar
[7]Cellina, A. and Marchi, M.V., ‘Nonconvex perturbations of mamimal monotone differential inclusions‘, Israel J. Math. 46 (1983), 111.CrossRefGoogle Scholar
[8]Cellina, A. and Staicu, V., ‘On evolution equations having monotonicities of opposite sign’, J. Differential Equations 90 (1991), 7180.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), 211218.CrossRefGoogle Scholar
[11]Kato, T., ‘Nonlinear semigroups and evolution equations’, J. Math. Soc. Japan 19 (1976), 508520.Google Scholar
[12]Kravritis, D. and Papageorgiou, N.S., ‘Multivalued perturbations of subdifferential type evolution equations in Hilbert spaces’, J. Differential Equations 76 (1988), 238255.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), 525531.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), 658697.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), 165211.CrossRefGoogle Scholar
[17]Pascali, D. and Sburlan, S., Nonlinear mappings of monotone type (Sijthoff and Noordhoff International Publishers, Romania, 1978).CrossRefGoogle Scholar