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

Author(s): Junyu Wang
Journal: Proc. Amer. Math. Soc. 125 (1997), 2275-2283.
MSC (1991): Primary 34B15
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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.

References:

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2.: L. H. Erbe and H. Wang, On the existence of positive solutions of ordinary differential equations, Proc. Amer. Math. Soc. 120 (1994), 743-748. MR 94e:34025
3.: M. A. Krasnoselskii, Positive solutions of operator equations, Noordhoff, Gronignen, 1964. MR 31:6107
4.: Z. Yang and X. Fan, The existence of positive solutions of a class of two-order quasilinear boundary value problems, Natural Science Journal of Xiangtan University, 15 (1993), Suppl. 205-209. MR 95j:34037


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