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Structure of positive boundary blow-up solutions

Published online by Cambridge University Press:  12 July 2007

Zongming Guo
Zongming Guo
Affiliation:
Department of Mathematics, Henan Normal University, Xinxiang 453002, People's Republic of China (guozm@public.xxptt.ha.cn)
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Abstract

The structure of positive boundary blow-up solutions to semilinear problems of the form −Δu = λf(u) in Ω, u = ∞ on ∂Ω, Ω ⊂ RN a bounded smooth domain, is studied for a class of nonlinearities f ∈ C1 ([0, ∞)\{z2}) satisfying f (0) = f(z1) = f (z2) = 0 with 0 < z1 < z2, f < 0 in (0, z1)∪(z2, ∞), f > 0 in (z1, z2). Two positive boundary-layer solutions and infinitely many positive spike-layer solutions are obtained for λ sufficiently large.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 134 , Issue 5 , October 2004 , pp. 923 - 938
Copyright
Copyright © Royal Society of Edinburgh 2004

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