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The obstacle problem and partial differential equations with discontinuous nonlinearities
Author(s) -
Chang K. C.
Publication year - 1980
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.3160330203
Subject(s) - mathematics , multiplicity (mathematics) , eigenvalues and eigenvectors , nonlinear system , boundary value problem , mathematical analysis , physics , quantum mechanics
summary:In the paper we study the topological structure of the solution set of a class of nonlinear evolution inclusions. First we show that it is nonempty and compact in certain function spaces and that it depends in an upper semicontinuous way on the initial condition. Then by strengthening the hypothesis on the orientor field $F(t,x)$, we are able to show that the solution set is in fact an $R_\delta $-set. Finally some applications to infinite dimensional control systems are also presented