On limiting transition in impulse boundary value problems for equations of neutral type
The main result of the paper under review is to prove the following theorem: Let the set \(\bigcup_{k=1}^ \infty T_ k P_ k A\) be relatively compact in \({\mathfrak L}_ n\) for all bounded \(A\subset DS^ n (m,0)\). For every fixed \(z\in {\mathfrak L}_ n\), let the sequence \((S_ k z)^ \infty_{k =1}\) be also relatively compact in \({\mathfrak L}_ n\). Further, we assume other additional conditions. Then, if the set \(M\) is bounded, it is also \({\mathcal P}\)-compact. Remark. About \(DS^ n (m,0)\) see the following: \textit{G. M. Vajnikko}, Itogi Nauki Tekh., Ser. Mat. Anal. 16, 5-53 (1979; Zbl 0582.65046).
scientific article; zbMATH DE number 484342