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

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Abstract

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.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Southwest University, Chongqing, 400715, People’s Republic of China

    Rui-Ting Jiang & Chun-Lei Tang

Authors
  1. Rui-Ting Jiang
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  2. Chun-Lei Tang
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Corresponding author

Correspondence to Chun-Lei Tang.

Additional information

Communicated by Syakila Ahmad.

Supported by National Natural Science Foundation of China (No. 11471267).

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Jiang, RT., Tang, CL. Positive Solutions for Elliptic Problems Involving Hardy–Sobolev–Maz’ya Terms. Bull. Malays. Math. Sci. Soc. 42, 2333–2359 (2019). https://doi.org/10.1007/s40840-018-0603-3

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  • DOI: https://doi.org/10.1007/s40840-018-0603-3

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