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On a Liouville-type equation with sign-changing weight

Published online by Cambridge University Press:  13 March 2009

Bernhard Ruf  and
Pedro Ubilla
Bernhard Ruf
Affiliation:
Dipartimento de Matematica, Università degli Studi, Via Saldini 50, 20133 Milan, Italy (ruf@mat.unimi.it)
Pedro Ubilla
Affiliation:
Departamento de Matemática y CC, Universidad de Santiago de Chile, Casilla 307, Correo 2, Santiago, Chile (pubilla@usach.cl)
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Abstract

We study the existence, nonexistence and multiplicity of non-negative solutions for the family of problems

where Ω is a bounded domain in ℝ2 and λ > 0 is a parameter. The coefficient a(x) is permitted to change sign. The techniques used in the proofs are a combination of upper and lower solutions, the Trudinger–Moser inequality and variational methods. Note that when f(x, u) = 0 the equation is of Liouville type.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 139 , Issue 1 , February 2009 , pp. 183 - 192
Copyright
Copyright © Royal Society of Edinburgh 2009

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