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Proceedings of the American Mathematical Society

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The existence of positive solutions
for the one-dimensional $p$-Laplacian

Author: Junyu Wang
Journal: Proc. Amer. Math. Soc. 125 (1997), 2275-2283
MSC (1991): Primary 34B15
MathSciNet review: 1423340
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Abstract: In this paper we study the existence of positive solutions of the equation $(g(u'))'+a(t)f(u)=0$, where $g(v)=|v|^{p-2}v$, $p>1$, subject to nonlinear boundary conditions. We show the existence of at least one positive solution by a simple application of a Fixed Point Theorem in cones and the Arzela-Ascoli Theorem.

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Additional Information

Junyu Wang
Affiliation: Department of Mathematics, Jilin University, Changchun 130023, People’s Republic of China

Keywords: One-dimensional $p$-Laplacian, positive solution, existence, concavity, fixed point theorem in cones.
Received by editor(s): December 6, 1995
Additional Notes: The author was supported by NNSF of China
Communicated by: Hal L. Smith
Article copyright: © Copyright 1997 American Mathematical Society