Solvability of a (p, n-p)-type multi-point boundary-value problem for higher-order differential equations
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In 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.
CitationLiu, Y., & Ge, W. (2003). Solvability of a (p, n-p)-type multi-point boundary-value problem for higher-order differential equations. Electronic Journal of Differential Equations, 2003(120), pp. 1-19.
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