Deimling K. Multivalued Differential Equations

Berlin: W. de Gruyter, 1992. — 272 p.The title of the book reveals that our subject (also named differential inclusions) has something to do with differential equations, say x' = f(t, x) on some interval J c U for differentiate functions x( •) on J with values in some space X, i.e. just one equation in case X = R, but a system of n equations x- = f,(t, xl... x„) for i = 1 n in case X = W with n > 2. perhaps the first order version of an n-th order equation x("» = f(t, x, x'... x*-l)) for some n > 2, maybe the abstract version of a partial differential equation in case X is an infinite-dimensional Banach space. So we assume that the reader has seen some simple examples (dim X > 2 is sufficient) from applied science where the unknown x(-) also has to satisfy certain initial/boundary conditions, or is required to be periodic in case /(•, x) is periodic, etc. In such elementary cases / is at least continuous, if not Lipschitz or even continuously differentiable.
Keywords: Multivalued maps, multivalued differential equations, discontinuous differential equations, fixed points of multivalued maps, control theory, treshold and dry friction problems