The existence of positive solutions for the one-dimensional \(p\)-Laplacian. (English) Zbl 0884.34032

Wang, Junyu

Proc. Am. Math. Soc. 125, No. 8, 2275-2283 (1997).

Summary: We study the existence of positive solutions of the equation \[ \bigl(g(u')\bigr)'+a(t)f(u)=0, \] 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.

MSC:

34B15

Nonlinear boundary value problems for ordinary differential equations

Keywords:

one-dimensional \(p\)-Laplacian; positive solution; existence; concavity; fixed point theorem in cones

References:

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