On solutions of differential inclusions with impulse structure (Q446317)

Consider the differential inclusion NEWLINE\[NEWLINE \dot{x}\in F(t,x)+ p(t), \tag{1} NEWLINE\]NEWLINE where \(x \in\mathbb R^{n}\), \(t\in [t_{0}, t_{1}]\).NEWLINENEWLINEThe multimapping \(F(\cdot,\cdot)\) is compact and convex valued on \([t_{0}, t_{1}]\times\mathbb R^{n}\), \(p(t)\) is the generalized derivative of a measurable and bounded function \(w(t)\). The existence of solutions of the differential inclusion (1) is proved.