Positive Solutions for Elliptic Problems Involving Hardy–Sobolev–Maz’ya Terms



In the present paper, we study the semilinear elliptic problem \(\displaystyle -\Delta u -\mu \frac{u}{|y|^{2}}=\frac{|u|^{2^{*}(s)-2}u}{|y|^{s}}+ f(x,u)\) in bounded domain. Replacing the Ambrosetti–Rabinowitz condition by general superquadratic assumptions and the nonquadratic assumption, we establish the existence results of positive solutions.


Positive solutions Hardy–Sobolev–Maz’ya terms Hardy–Sobolev critical exponents Mountain Pass Lemma Local Palais–Smale condition 


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Copyright information

© Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2018

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsSouthwest UniversityChongqingPeople’s Republic of China

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