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The Method of Upper and Lower Solutions for a Lidstone Boundary Value Problem
 Yanping Guo,
 Ying Gao
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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] × 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.
The project is supported by the Natural Science Foundation of China (10371030), by the Science and Technology Research development foundation for Universities of Shanxi Province (20051254), and by the Doctoral Program Foundation of Hebei Province (B2004204).
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 Title
 The Method of Upper and Lower Solutions for a Lidstone Boundary Value Problem
 Journal

Czechoslovak Mathematical Journal
Volume 55, Issue 3 , pp 639652
 Cover Date
 20050901
 DOI
 10.1007/s1058700500518
 Print ISSN
 00114642
 Online ISSN
 15729141
 Publisher
 Kluwer Academic PublishersConsultants Bureau
 Additional Links
 Topics
 Keywords

 nparameter eigenvalue problem
 Lidstone boundary value problem
 lower solution
 upper solution
 Authors

 Yanping Guo ^{(1)} ^{(2)}
 Ying Gao ^{(3)}
 Author Affiliations

 1. College of Science, Hebei University of Science and Technology, Shijiazhuang, Hebei, 050018, P.R. China
 2. College of Physical and Environmental Oceanography, Ocean University of China, Qingdao, 266003, P. R. China
 3. Department of Mathematics, Yanbei Normal Institute, Datong, Shanxi, 037000, P. R. China