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Zeitschrift für Analysis und ihre Anwendungen


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Volume 37, Issue 2, 2018, pp. 189–207
DOI: 10.4171/ZAA/1609

Published online: 2018-03-29

Topological Structure of Solutions Sets for Semilinear Evolution Inclusions

Yong Zhou[1] and Li Peng[2]

(1) Xiangtan University, China
(2) Xiangtan University, China

This paper deals with a semilinear evolution inclusion involving a nondensely de fined closed linear operator satisfying the Hille–Yosida condition and source term of multivalued type in Banach spaces. The topological structure of the set of solutions is investigated in the case that semigroup is noncompact. It is shown that the solution set is nonempty, compact and an $R_\delta$-set. It is proved on compact intervals and then, using the inverse limit method, obtained on non-compact intervals. As a sample of application, we consider a parabolic partial di fferential inclusion at end of the paper.

Keywords: Evolution inclusions, solution sets, noncompact semigroup, topological structure, Hille–Yosida condition

Zhou Yong, Peng Li: Topological Structure of Solutions Sets for Semilinear Evolution Inclusions. Z. Anal. Anwend. 37 (2018), 189-207. doi: 10.4171/ZAA/1609