Abstract and Applied Analysis
Volume 2005 (2005), Issue 6, Pages 639-653
doi:10.1155/AAA.2005.639

Critical singular problems on unbounded domains

D. C. de Morais Filho1 and O. H. Miyagaki2

1Departamento de Matemática e Estatística, Universidade Federal de Campina Grande, Caixa Postal 10044, Campina Grande 58109-970, PB, Brazil
2Departamento de Matemática, Universidade Federal de Viçosa, Viçosa 36571-000, MG, Brazil

Received 30 April 2004

Copyright © 2005 D. C. de Morais Filho and O. H. Miyagaki. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We present some results of existence for the following problem: −Δu=a(x)g(u)+u|u|2∗−2, x∈ℝN(N≥3), u∈D1,2(ℝN), where the function a is a sign-changing function with a singularity at the origin and g has growth up to the Sobolev critical exponent 2∗=2N/(N−2).