Generalized averages for solutions of nonlinear operators (Q1588426)

The author considers the twopoint boundary value problem \[ \bigl( \varphi(u') \bigr)'+f(u)=0,\;u(0)=u(T)=0, \] with \(\varphi\in C'(\mathbb{R},\mathbb{R})\), \(\varphi\) is strictly increasing, \(\varphi(\mathbb{R}) =\mathbb{R}\) and \(\varphi(0)=0\). By a suitable transformation, the equation is reduced to a simple form and known eigenvalue problem results are applied to obtain a generalized average result for positive solutions.