Positive solutions of a Lidstone boundary value problem with variable coefficient function

Article

Abstract

We establish the existence of positive solutions of the Lidstone boundary value problem
$$\begin{array}{rcl}(-1)^{n}u^{(2n)}&=&\lambda a(t)f(u),\quad 0<t<1,\\[3pt]u^{(2i)}(0)&=&u^{(2i)}(1)=0,\quad 0\leq i\leq n-1\end{array}$$
for all sufficiently small positive real λ, where the function a may change sign in [0,1] and the function f:[0,∞)→R satisfies f(0)>0. We also show that our assumption is not vacuous.

Keywords

Lidstone boundary value problem Positive solution Leray-Schauder fixed point theorem 

Mathematics Subject Classification (2000)

34B16 

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Copyright information

© KSCAM and Springer-Verlag 2008

Authors and Affiliations

  1. 1.School of Mathematics, Physics and Software EngineeringLanzhou Jiaotong UniversityLanzhouPeople’s Republic of China
  2. 2.Department of MathematicsTsing Hua UniversityHsinchuTaiwan, R.O. China

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