Compactness theorems for abstract evolution problems (Q698281)

Consider the evolution problem defined by a family of unbounded, multivalued, dissipative, nonlinear operators in a Banach space. The author gives conditions under which, for a given starting point, the problem has either no bounded solution or a bounded solution with precompact trajectory. He extends and supplements results by \textit{A. Pazy} [Isr. J. Math. 20, 23-36 (1975; Zbl 0305.47022)], \textit{C. M. Dafermos} and \textit{M. Slemrod} [J. Funct. Anal. 13, 97-106 (1973; Zbl 0267.34062)], and \textit{G. F. Webb} [Proc. Roy. Soc. Edinb., Sect. A 84, 19-33 (1979; Zbl 0414.34042)].