Czechoslovak Mathematical Journal

, Volume 55, Issue 3, pp 639–652

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

  • Yanping Guo
  • Ying Gao
Article

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

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

Authors and Affiliations

  • Yanping Guo
    • 1
    • 2
  • Ying Gao
    • 3
  1. 1.College of ScienceHebei University of Science and TechnologyShijiazhuang, HebeiP.R. China
  2. 2.College of Physical and Environmental OceanographyOcean University of ChinaQingdaoP. R. China
  3. 3.Department of MathematicsYanbei Normal InstituteDatong, ShanxiP. R. China

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