Existence and uniqueness of solutionsto first-order multipoint boundary value problems Original Research Article

In this paper, we give existence and uniqueness results for solutions of multipoint boundary value problems of the form View the MathML sourcexʹ=f(t,x(t))+e(t),t∈(0,1),∑j=1mAjx(ηj)=0, Turn MathJax on where ƒ : [0,1] × Rn → Rn is a Carathéodory function, Ajs (j = 1, 2,, m) are constant square matrices of order n, 0 < η1 η2 << ηm−1, < ηm ⪯ 1, and e(t) ∈ L1([0,1], Rn). The existence of solutions is proven by the coincidence degree theory. As an application, we also give one example to demonstrate our results.