Electron. J. Diff. Eqns., Vol. 2005(2005), No. 19, pp. 1-21.

Existence and uniqueness of solutions to a super-linear three-point boundary-value problem

Bruce Calvert, Chaitan P. Gupta

Abstract:
In previous papers, degree theory for nonlinear operators has been used to study a class of three-point boundary-value problems for second order ordinary differential equations having a super-linear term, and existence of a sequence of solutions has been shown. In this paper, we forgo the previous approach for the shooting method, which gives a drastically simpler existence theory, with less assumptions, and easy calculation of solutions. We even obtain uniqueness in the simplest case.

Submitted November 16, 2004. Published February 7, 2005.
Math Subject Classifications: 34B10, 34B15.
Key Words: Super-linear; three-point boundary-value problem.

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Bruce Calvert
Department of Mathematics
University of Auckland
Auckland, New Zealand
email: calvert@math.auckland.ac.nz
Chaitan P. Gupta
Department of Mathematics, 084
University of Nevada,
Reno, NV 89557, USA
email: gupta@unr.edu

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