Solution curves and exact multiplicity results for 2mth order boundary value problems

Rehana Bari, Bryan P. Rynne

Research output: Contribution to journalArticle

Abstract

For any integer m = 2, we consider the 2mth order boundary value problem (-1)m u(2m) (x) = ?g(u(x))u(x), x ? (-1, 1), u(i) (-1) = u(i) (1) = 0, i = 0,..., m - 1, where ? ? R, and the function g: R ? R is C1 and satisfies g(0) > 0, ±g' (?) > 0, ±? > 0, together with some further conditions as ? ? 8. We obtain curves of nontrivial solutions of this problem, bifurcating from u = 0 at the eigenvalues of the linearised problem, and obtain the exact number of solutions of the problem for ? lying in various intervals in R. © 2003 Elsevier Inc. All rights reserved.

Original languageEnglish
Pages (from-to)17-22
Number of pages6
JournalJournal of Mathematical Analysis and Applications
Volume292
Issue number1
DOIs
Publication statusPublished - 1 Apr 2004

Keywords

  • Exact multiplicity
  • Nonlinear boundary value problems
  • Ordinary differential equations

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