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Zeitschrift für Analysis und ihre Anwendungen


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Volume 18, Issue 3, 1999, pp. 525–537
DOI: 10.4171/ZAA/896

Published online: 1999-09-30

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

Yuanji Cheng[1]

(1) University of Malmö, Sweden

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.

Keywords: Boundary blow-up, multiplicity, concave and convex nonhinearily

Cheng Yuanji: Some Surprising Results on a One-Dimensional Elliptic Boundary Value Blow-Up Problem. Z. Anal. Anwend. 18 (1999), 525-537. doi: 10.4171/ZAA/896