Abstract and Applied Analysis

Critical singular problems on unbounded domains

Abstract

We present some results of existence for the following problem: $-\!\Delta u\!=\!\!a(x)g(u)\!+\!u|u|^{2^{*}-2}$, $x\in \mathbb{R}^{N}\ (N\geq 3)$, $u\in D^{1,2}(\mathbb{R}^{N})$, 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 $2^{*}=2N/(N-2)$.

Article information

Source
Abstr. Appl. Anal., Volume 2005, Number 6 (2005), 639-653.

Dates
First available in Project Euclid: 3 October 2005

https://projecteuclid.org/euclid.aaa/1128345943

Digital Object Identifier
doi:10.1155/AAA.2005.639

Mathematical Reviews number (MathSciNet)
MR2202953

Zentralblatt MATH identifier
1128.35047

Citation

Filho, D. C. de Morais; Miyagaki, O. H. Critical singular problems on unbounded domains. Abstr. Appl. Anal. 2005 (2005), no. 6, 639--653. doi:10.1155/AAA.2005.639. https://projecteuclid.org/euclid.aaa/1128345943

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