Abstract and Applied Analysis

Existence of Multiple Solutions for a Singular Elliptic Problem with Critical Sobolev Exponent

Zonghu Xiu

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Abstract

We consider the existence of multiple solutions of the singular elliptic problem - div ( | x | - a p | u | p - 2 u ) + | u | p - 2 u / | x | ( a + 1 ) p = f | u | r - 2 u + h | u | s - 2 u + | x | - b p * | u | p * - 2 u , u ( x ) 0 as | x | + , where x N , 1 < p < N , a < ( N - p ) / p , a b a + 1 , r , s > 1 , p * = N p / ( N - p d ) , d = a + 1 - b . By the variational method and the theory of genus, we prove that the above-mentioned problem has infinitely many solutions when some conditions are satisfied.

Article information

Source
Abstr. Appl. Anal., Volume 2012, Special Issue (2012), Article ID 806397, 15 pages.

Dates
First available in Project Euclid: 5 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1365168318

Digital Object Identifier
doi:10.1155/2012/806397

Mathematical Reviews number (MathSciNet)
MR2999909

Zentralblatt MATH identifier
1261.35068

Citation

Xiu, Zonghu. Existence of Multiple Solutions for a Singular Elliptic Problem with Critical Sobolev Exponent. Abstr. Appl. Anal. 2012, Special Issue (2012), Article ID 806397, 15 pages. doi:10.1155/2012/806397. https://projecteuclid.org/euclid.aaa/1365168318


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