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

### Yuanji Cheng

University of Malmö, Sweden

## Abstract

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

$\Delta_p u = f(u) \ \ (a < t < b)$

$u(a) = u(b) = +\infty$

where $\Delta_p u = (|u'{t}|^{p–2} u'(t))'$ 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.

## Cite this article

Yuanji Cheng, Some Surprising Results on a One-Dimensional Elliptic Boundary Value Blow-Up Problem. Z. Anal. Anwend. 18 (1999), no. 3, pp. 525–537

DOI 10.4171/ZAA/896