Some higher-order multi-point boundary value problem at resonance

  • Authors:

  • Zengji Du;Xiaojie Lin;Weigao Ge

  • Affiliations:

  • Department of Mathematics, Beijing Institute of Technology Beijing 100081, People's Republic of China;Department of Mathematics, Xuzhou Normal University, Xuzhou, 221116, People's Republic of China;Department of Mathematics, Beijing Institute of Technology Beijing 100081, People's Republic of China

  • Venue:
  • Journal of Computational and Applied Mathematics
  • Year:
  • 2005

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Abstract

This paper deals with the existence of solutions for the following nth order multi-point boundary value problem at resonance x(n)(t) = f(t, x(t), x'(t),..., x(n-1)(t)) + e(t), t ∈ (0, 1), x(0) = Σi=1m-2 αix(ξi), x'(0) =...= x(n-2) (0) = 0, x(1) = x(η), where f : [0, 1] × Rn → R is a continuous function, e ∈ L1[0, 1], αi ∈ R(1 ≤ i ≤ m - 2), 0 1 2 m-2