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

In the present paper, we study the semilinear elliptic problem - Δ u - μ u | y | 2 = | 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...

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Bibliographic Details
Published in:Bulletin of the Malaysian Mathematical Sciences Society 2019-09, Vol.42 (5), p.2333-2359
Main Authors: Jiang, Rui-Ting, Tang, Chun-Lei
Format: Article
Language:English
Subjects:
Applications of Mathematics
Mathematics
Mathematics and Statistics
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Summary:In the present paper, we study the semilinear elliptic problem - Δ u - μ u | y | 2 = | 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.
ISSN:0126-6705
2180-4206
DOI:10.1007/s40840-018-0603-3