Asymptotic and integral equivalence of multivalued differential systems (Q749750)

There are introduced notions of a g-bounded set \(A\subset L^ p(J)\) and a g-compact operator T which maps A into a Banach space Y. This allows us to strengthen several theorems which are useful in the theory of multivalued mappings. Then it is studied the asymptotic and \((\psi,p)\)- integral equivalence of differential systems of the form \[ (a)\quad x'(t)\in A(t)x(t)+F(t,x(t),Sx(t)),\quad (b)\quad y'(t)=A(t)y(t). \] Finally a theorem on oscillatory behavior of (a) is proved. The paper also generalizes a \textit{W. Sobieszek} - \textit{P. Kowalski's} theorem on the semicompactness of multivalued mappings [Demonstr. Math. 11, 1053- 1063 (1978; Zbl 0408.54001)].