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- W2597376674 abstract "In this paper, we first present an impulsive version of Filippov'sTheorem for first-order semilinear functional differentialinclusions of the form:$$cases(y'-Ay) in F(t,y_t) &text{a.e. } tin Jsetminus {t_{1},ldots,t_{m}},y(t^+_{k})-y(t^-_k)=I_{k}(y(t_{k}^{-})) &text{for } k=1,ldots,m,y(t)=phi(t) &text{for } tin[-r,0],endcases$$where $J=[0,b]$, $A$ is the infinitesimal generator of a$C_0$-semigroup on a separable Banach space $E$ and $F$ is aset-valued map. The functions $I_k$ characterize the jump of thesolutions at impulse points $t_k$ ($k=1,ldots,m$). Then theconvexified problem is considered and a Filippov-Wa{plr z}ewski resultis proved. Further to several existence results, the topologicalstructure of solution sets -- closeness and compactness -- is alsoinvestigated. Some results from topological fixed point theorytogether with notions of measure on noncompactness are used.Finally, some geometric properties of solution sets, AR,$R_delta$-contractibility and acyclicity, corresponding toAronszajn-Browder-Gupta type results, are obtained." @default.
- W2597376674 created "2017-03-23" @default.
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- W2597376674 date "2008-12-01" @default.
- W2597376674 modified "2023-10-06" @default.
- W2597376674 title "Filippov-Ważewski theorems and structure of solution sets for first order impulsive semilinear functional differential inclusions" @default.
- W2597376674 doi "https://doi.org/10.12775/tmna.2008.049" @default.
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