Limit Theorems for Differential Systems with Multipoint Boundary Conditions in Sobolev Spaces

Abstract

Abstract The most general class of multipoint inhomogeneous boundary-value problems for systems of linear ordinary differential equations of arbitrary order $$r\ge 1$$ r ≥ 1 is investigated, whose solutions belong to a given Sobolev space $$W_p^{n+r}$$ W p n + r , where $$n\ge 0$$ n ≥ 0 and $$1\le p\le \infty $$ 1 ≤ p ≤ ∞ . The boundary conditions in these problems contain Caputo derivatives of fractional or integer orders, which may exceed the order of the equations of the differential system. Constructive sufficient conditions are established under which the solutions of these problems are continuous in the Sobolev space $$W_p^{n+r}$$ W p n + r with respect to a parameter from an abstract metric space.