# The Method of Upper and Lower Solutions for a Lidstone Boundary Value Problem

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- Received:

DOI: 10.1007/s10587-005-0051-8

- Cite this article as:
- Guo, Y. & Gao, Y. Czech Math J (2005) 55: 639. doi:10.1007/s10587-005-0051-8

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## Abstract

In this paper we develop the monotone method in the presence of upper and lower solutions for the 2nd order Lidstone boundary value problem where

$$\begin{array}{*{20}c} {u^{(2n)} (t) = f(t,\;u(t),\;u''(t),...,u^{(2(n - 1))} (t)),\quad 0 < t < 1,} \\ {u^{(2i)} (0) = u^{(2i)} (1) = 0,\quad 0 \leqslant i \leqslant n - 1,} \\ \end{array}$$

*f*: [0, 1] × ℝ^{n}→ ℝ is continuous. We obtain sufficient conditions on*f*to guarantee the existence of solutions between a lower solution and an upper solution for the higher order boundary value problem.### Keywords

*n*-parameter eigenvalue problem Lidstone boundary value problem lower solution upper solution

## Copyright information

© Mathematical Institute, Academy of Sciences of Czech Republic 2005