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2012 Existence of Multiple Solutions for a Singular Elliptic Problem with Critical Sobolev Exponent
Zonghu Xiu
Abstr. Appl. Anal. 2012(SI07): 1-15 (2012). DOI: 10.1155/2012/806397

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.

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Zonghu Xiu. "Existence of Multiple Solutions for a Singular Elliptic Problem with Critical Sobolev Exponent." Abstr. Appl. Anal. 2012 (SI07) 1 - 15, 2012. https://doi.org/10.1155/2012/806397

Information

Published: 2012
First available in Project Euclid: 5 April 2013

zbMATH: 1261.35068
MathSciNet: MR2999909
Digital Object Identifier: 10.1155/2012/806397

Rights: Copyright © 2012 Hindawi

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Vol.2012 • No. SI07 • 2012
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