Vol. 1, No. 1, 2008
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Qualitative behavior and computation of multiple solutions of singular nonlinear boundary value problems

Grey Ballard & John Baxley

Vol. 1 (2008), No. 1, 21-31
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

Primary: 34B16, 65L10
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