Smoothness of solutions with respect to multi-strip integral boundary conditions for nth order ordinary differential equations

Abstract

Under certain conditions, solutions of the boundary value problem y⁽ⁿ⁾ = f(x,y,y',...,y^(n-1)), a < x < b, y^(i-1)(x₁) = y_i, i=1,...,n-1, y(x₂) ∑ _i=1^mγ_i ∫ _ξi^η_iy(x)dx=yⁿ, a<x₁<ξ₁<η₁<ξ₂<η₂<...<ξ_m<η_m<x₂<b, are differentiated with respect to the boundary conditions.