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Acta Mathematicae Applicatae Sinica, English Series 2012, Vol. 28 Issue (1) :157-164    DOI: 10.1007/s10255-012-0131-0
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Singular Quasilinear Elliptic Problems with Indefinite Weights and Critical Potential
Gao JIA, Qing ZHAO, Chun-yan DAI
College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China
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Abstract The Dirichlet problem for a quasilinear sub-critical inhomogeneous elliptic equation with critical potential and singular coefficients, which has indefinite weights in RN, is studied in this paper. We discuss the corresponding eigenvalue problems by the variational techniques and Picone’s identity, and obtain the existence of non-trivial solutions for the inhomogeneous Dirichlet problem by using Hardy inequality, Mountain Pass Lemma in conjunction with the property of eigenvalues.  
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KeywordsPicone’s identity   Hardy inequality   critical potential   Mountain Pass Lemma     
Abstract: The Dirichlet problem for a quasilinear sub-critical inhomogeneous elliptic equation with critical potential and singular coefficients, which has indefinite weights in RN, is studied in this paper. We discuss the corresponding eigenvalue problems by the variational techniques and Picone’s identity, and obtain the existence of non-trivial solutions for the inhomogeneous Dirichlet problem by using Hardy inequality, Mountain Pass Lemma in conjunction with the property of eigenvalues.  
KeywordsPicone’s identity,   Hardy inequality,   critical potential,   Mountain Pass Lemma     
Received: 2009-03-06;
Fund:

Supported by the National Natural Science Foundation of China (No. 11171220) and Shanghai Leading Academic Discipline Project (No. S30501).

Corresponding Authors: Gao JIA     Email: gaojia@usst.edu.cn, gaojia79@yahoo.com.cn
Cite this article:   
.Singular Quasilinear Elliptic Problems with Indefinite Weights and Critical Potential[J]  Acta Mathematicae Applicatae Sinica, English Serie, 2012,V28(1): 157-164
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http://www.applmath.com.cn/jweb_yysxxb_en/EN/10.1007/s10255-012-0131-0      或     http://www.applmath.com.cn/jweb_yysxxb_en/EN/Y2012/V28/I1/157
 
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