Vol. 1, No. 1, 2008
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ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
Qualitative behavior and computation of multiple solutions of singular nonlinear boundary value problems

Grey Ballard and John Baxley
Vol. 1 (2008), No. 1, 21–31
DOI: 10.2140/involve.2008.1.21
Abstract

We consider boundary value problems of the form

y′′ = − f(t,y), y(0) = 0, y(1) = 0,

motivated by examples where f(t,y) = ϕ(t)g(y) and g(y) behave like y−λ (λ > 0) as y → 0+. We explore conditions under which such problems have multiple positive solutions, investigate qualitative behavior of these solutions, and discuss computational methods for approximating the solutions.
Keywords
singular nonlinear boundary value problems, multiple solutions, shooting, computation, qualitative behavior
Mathematical Subject Classification 2000
Primary: 34B16, 65L10
Milestones
Received: 28 October 2007
Accepted: 28 October 2007
Published: 28 February 2008
Authors
Grey Ballard
Department of Mathematics
Wake Forest University
Winston-Salem, NC 27106
United States
John Baxley
Department of Mathematics
Wake Forest University
Winston-Salem, NC 27106
United States