Singular Quasilinear Elliptic Problems with Indefinite Weights and Critical Potential

作     者：Gao JIA Qing ZHAO Chun-yan DAI 

作者机构：College of ScienceUniversity of Shanghai for Science and TechnologyShanghai 200093China 

出 版 物：《Acta Mathematicae Applicatae Sinica》 (应用数学学报（英文版）)

年 卷 期：2012年第28卷第1期

页      面：157-164页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

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

主　　题：Picone's identity Hardy inequality critical potential Mountain Pass Lemma 

摘      要：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.