I. Kiguradze, B. Puza, I. P. Stavroulakis

On Singular Boundary Value Problems for Functional Differential Equations of Higher Order

Sufficient conditions are established for the solvability of the boundary value problem $$ x^{(n)}(t)=f(x)(t), \;\;\; h_i(x)=0 \;\; (i=1,\dots,n), $$ where $f$ is an operator ($h_i$ $(i=1,\dots,n)$ are operators) acting from some subspace of the space of $(n-1)$-times differentiable on the interval $]a,b[$ $m$-dimensional vector functions into the space of locally integrable on $]a,b[$ $m$-dimensional vector functions (into the space $\bR^m$).