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

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.


34B15 Nonlinear boundary value problems for ordinary differential equations
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