Nonlinear singular multipoint boundary value problems

Joseph W Jerome*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

Let Λ be a linear differential operator on (a, b) of order 2m with leading coefficient possessing an integrable reciprocal. Global Cm‐1(a, b) solutions are shown to exist for certain nonlinear multipoint boundary value problems of the form A u = F(u, …, um‐1, where linear combinations of derivatives through order m – 1 are specified at points interior to (a, b). The associated linear problem is completely solved through the construction of an appropriate Green's function which determines a compact operator G = A−1. The linear eigenvalue problem is examined and a complete orthonormal system exhibited in L2(a, b). Solutions of the nonlinear problem are obtained by exhibiting fixed points for the operator GF.

Original languageEnglish (US)
Pages (from-to)31-38
Number of pages8
JournalZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik
Volume53
Issue number1
DOIs
StatePublished - Jan 1 1973

ASJC Scopus subject areas

  • Computational Mechanics
  • Applied Mathematics

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