Electron. J. Diff. Eqns., Vol. 1995(1995), No. 03, pp. 1-8.

Positive Solutions for Higher Order Ordinary Differential Equations

Paul W. Eloe & Johnny Henderson

Abstract:
Solutions that are positive with respect to a cone are obtained for the boundary value problem, $u^{(n)} + a(t)f(u) = 0$, $u^{(i)}(0) = u^{(n-2)}(1)= 0$, $0 \leq i \leq n-2$, in the cases that $f$ is either superlinear or sublinear. The methods involve application of a fixed point theorem for operators on a cone.

Submitted December 4, 1994. Published March 2, 1995.
Math Subject Classification: 34B15. Key words: Boundary value problems, positive solutions, superlinear and sublinear, operators on a cone.

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Paul W. Eloe
Department of Mathematics, University of Dayton, Dayton, OH 45469-2316 USA
e-mail: Paul.Eloe@notes.udayton.edu

Johnny Henderson
Discrete and Statistical Sciences, Auburn University, Auburn, AL 36849-5307 USA
e-mail: hendej2@mail.auburn.edu

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