Some Surprising Results on a One-Dimensional Elliptic Boundary Value Blow-Up Problem

Abstract

In this paper we consider the one-dimensional elliptic boundary blow-up problem

where ${\Delta }_{p}u=(|u^{\prime }t{|}^{p–2}{u}^{\prime }(t){)}^{\prime }$ is the usual $p$-Laplace operator. We show that the structure of the solutions can be very rich even for a simple function $f$ which gives a leading that a similar result might hold also in higher dimensional spaces.