Abstract and Applied Analysis

$N$-Laplacian equations in $\mathbb{R}^N$ with critical growth

João Marcos B. do Ó

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Abstract

We study the existence of nontrivial solutions to the following problem: {uW1,N(N),u0anddiv(|u|N2u)+a(x)|u|N2u=f(x,u)inN(N2), where a is a continuous function which is coercive, i.e., a(x)as|x| and the nonlinearity f behaves like exp(α|u|N/(N1)) when |u|.

Article information

Source
Abstr. Appl. Anal., Volume 2, Number 3-4 (1997), 301-315.

Dates
First available in Project Euclid: 14 April 2003

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1050355240

Digital Object Identifier
doi:10.1155/S1085337597000419

Mathematical Reviews number (MathSciNet)
MR1704875

Zentralblatt MATH identifier
0932.35076

Subjects
Primary: 35A15: Variational methods 35J60

Keywords
Elliptic equations $p$-Laplacian critical growth Mountain Pass theorem Trudinger-Moser inequality

Citation

B. do Ó, João Marcos. $N$-Laplacian equations in $\mathbb{R}^N$ with critical growth. Abstr. Appl. Anal. 2 (1997), no. 3-4, 301--315. doi:10.1155/S1085337597000419. https://projecteuclid.org/euclid.aaa/1050355240


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