On a class of implicit differential inclusions
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- by Zouhua Ding PDF
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Abstract:
The existence of solutions is established for implicit differential inclusions $M(x’)+C(x)\owns 0$ in $R^n$ involving the sum of a maximal monotone mapping $M$ and an upper semicontinuous mapping $C$ with compact, closed values. A question of Wenzel is answered in the affirmative.References
- G. Wenzel, On a class of implicit differential inclusions, J. Differential Equations 63 (1986), no. 2, 162–182. MR 848266, DOI 10.1016/0022-0396(86)90046-X
- Jean-Pierre Aubin and Arrigo Cellina, Differential inclusions, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 264, Springer-Verlag, Berlin, 1984. Set-valued maps and viability theory. MR 755330, DOI 10.1007/978-3-642-69512-4
- C. J. Himmelberg and F. S. Van Vleck, A note on the solution sets of differential inclusions, Rocky Mountain J. Math. 12 (1982), no. 4, 621–625. MR 683856, DOI 10.1216/RMJ-1982-12-4-621
Additional Information
- Zouhua Ding
- Affiliation: Department of Mathematics, University of South Florida, Tampa, Florida 33620-5700
- Email: ding@chuma.usf.edu
- Received by editor(s): September 1, 1992
- Received by editor(s) in revised form: March 1, 1994
- Communicated by: Dale Alspach
- © Copyright 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 124 (1996), 745-749
- MSC (1991): Primary 34A60; Secondary 34A09
- DOI: https://doi.org/10.1090/S0002-9939-96-03402-8
- MathSciNet review: 1328345