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On a class of two-dimensional singular elliptic problems

Published online by Cambridge University Press:  12 July 2007

Paolo Caldiroli  and
Roberta Musina
Paolo Caldiroli
Affiliation:
Dipartimento di Matematica, Universita di Torino, via Carlo Alberto, 10-10123 Torino, Italy (caldiroli@dm.unito.it)
Roberta Musina
Affiliation:
Dipartimento di Matematica ed Informatica, Universita di Udine, via delle Scienze, 206-33100 Udine, Italy (musina@dimi.uniud.it)
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Abstract

We consider Dirichlet problems of the form −|x|αΔu = λu + g(u) in Ω, u = 0 on ∂Ω, where α, λ ∈ ℝ, g ∈ C(ℝ) is a superlinear and subcritical function, and Ω is a domain in ℝ2. We study the existence of positive solutions with respect to the values of the parameters α and λ, and according that 0 ∈ Ω or 0 ∈ ∂Ω, and that Ω is an exterior domain or not.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 131 , Issue 3 , June 2001 , pp. 479 - 497
Copyright
Copyright © Royal Society of Edinburgh 2001

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