JournalszaaVol. 18, No. 3pp. 525–537

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

  • Yuanji Cheng

    University of Malmö, Sweden
Some Surprising Results on a One-Dimensional Elliptic Boundary Value Blow-Up Problem cover
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Abstract

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

Δpu=f(u)  (a<t<b)\Delta_p u = f(u) \ \ (a < t < b)
u(a)=u(b)=+u(a) = u(b) = +\infty

where Δpu=(utp2u(t))\Delta_p u = (|u'{t}|^{p–2} u'(t))' is the usual pp-Laplace operator. We show that the structure of the solutions can be very rich even for a simple function ff 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