Liu, YujiGe, Weigao2021-01-292021-01-292003-12-01Liu, Y., & Ge, W. (2003). Solvability of a (p, n-p)-type multi-point boundary-value problem for higher-order differential equations. <i>Electronic Journal of Differential Equations, 2003</i>(120), pp. 1-19.1072-6691https://hdl.handle.net/10877/13171In this article, we study the differential equation (-1)n-p x(n) (t) = ƒ(t, x(t), x'(t),..., x(n-1) (t)), 0 < t < 1, subject to the multi-point boundary conditions x(i) (0) = 0 for i = 0, 1,..., p - 1, x(i) (1) = 0 for i = p + 1, ..., n - 1, ∑mi=1 αix(p) (ξi) = 0, where 1 ≤ p ≤ n - 1. We establish sufficient conditions for the existence of at least one solution at resonance and another at non-resonance. The emphasis in this paper is that ƒ depends on all higher-order derivatives. Examples are given to illustrate the main results of this article.Text19 pages1 file (.pdf)enAttribution 4.0 InternationalSolvabilityResonanceNon-resonanceMulti-point boundary-value problemHigher order differential equationArticle