On Nonhomogeneous Elliptic Equations with Critical Sobolev Exponent and Prescribed Singularities

In this paper we consider a class of nonhomogeneous elliptic equations involving multi-polar Hardy type potentials and a Sobolev critical nonlinearity in an open domain of ℝ N ,N≥ 3. By Ekeland’s Variational Principle and the Mountain Pass Lemma, we prove the existence of multiple solutions under su...

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Bibliographic Details
Published inTaiwanese journal of mathematics Vol. 20; no. 2; pp. 431 - 447
Main Authors Bouchekif, Mohammed, Messirdi, Sofiane
Format Journal Article
LanguageEnglish
Published Mathematical Society of the Republic of China 01.04.2016
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ISSN1027-5487
2224-6851
DOI10.11650/tjm.20.2016.5665

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Summary:In this paper we consider a class of nonhomogeneous elliptic equations involving multi-polar Hardy type potentials and a Sobolev critical nonlinearity in an open domain of ℝ N ,N≥ 3. By Ekeland’s Variational Principle and the Mountain Pass Lemma, we prove the existence of multiple solutions under sufficient conditions on the data and the considered parameters. 2010Mathematics Subject Classification. 35J20, 35J50, 35B33. Key words and phrases. Critical Sobolev exponent, Palais-Smale condition, Ekeland’s variational principle, Multi-singular potentials, Concentration compactness principle, Hardy inequality.
ISSN:1027-5487
2224-6851
DOI:10.11650/tjm.20.2016.5665