Solvability of a (p, n-p)-type multi-point boundary-value problem for higher-order differential equations
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Date
2003-12-01
Authors
Liu, Yuji
Ge, Weigao
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
Abstract
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.
Description
Keywords
Solvability, Resonance, Non-resonance, Multi-point boundary-value problem, Higher order differential equation
Citation
Liu, 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.
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Attribution 4.0 International