Nondensely defined evolution impulsive differential inclusions with nonlocal conditions.
The authors study a problem for evolution impulsive differential inclusions with nonlocal conditions of the form \(y'(t) \in Ay(t) + F(t,y(t))\), \(t \in J=[0,b]\), \(t \neq t_k\), \(k=1,\dots,m\), \(y(t_k^+)-y(t_k^-)= I_k(y(t_k^-))\), \(k=1,\dots,m\), \(y(0)+g(y)=y_0\), where \(A:D(A)\subset E \to E\) is a nondensely defined closed linear operator, \(F:J \times E \to P(E)\) is a multivalued map with nonempty values, \(g:C(J',E) \to E\) (\(J'=J-\{t_1,\dots,t_m\}\)), \(I_k:E \to \overline{D(A)} \) are functions, \(y_0 \in E\) and \(E\) is a separable Banach space. The authors establish sufficient conditions for the existence of integral solutions for the convex and for the nonconvex case by using fixed-point theorems and a selection theorem.
impulsive semilinear differential equation
scientific article; zbMATH DE number 2003909
scientific article