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Solvability of singular second order m-point boundary value problems of Dirichlet type

Published online by Cambridge University Press:  17 April 2009

Ruyun Ma
Affiliation:
Department of Mathematics, Northwest Normal University, Lanzhou 730070, Peoples Republic of China
Bevan Thompson
Affiliation:
Department of Mathematics, The University of Queensland, Brisbane Qld 4072, Australia
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Let f: [0, 1] × ℝ2 → ℝ be a function satisfying the Carathéodory conditions and t (1 − t) e (t) ∈ L1(0, 1). Let ai ∈ ℝ and ξi ∈ (0, 1) for i = 1, …, m − 2 where 0 < ξ1 < ξ2 < … < ξm−2 < 1. In this paper we study the existence of C[0, 1] solutions for the m-point boundary value problem The proof of our main result is based on the Leray-Schauder continuation theorem.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2005

References

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