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Fractional p-Laplacian Problem with Critical Stein–Weiss Type Term

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Abstract

The paper is concerned with the p-Laplacian minimizing problem with critical Stein–Weiss type term, and a nonlocal nonlinear equation involving fractional p-Laplacian operator and critical Stein–Weiss type term. Then main difficulty is hard to get the compactness of bounded minimizing sequence (and bounded Palais–Smale sequence). By the refined Sobolev inequality with Lorentz norm, we establish a abstract theorem, which is the relatively compactness result of bounded symmetric decreasing sequence. And then, as applications, we prove the existence, decay and regular results for the problems.

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Acknowledgements

Y. Su is supported by the National Natural Science Foundation of China (Grant No. 12101006).

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  1. School of Mathematics and Big Data, Anhui University of Science and Technology, Huainan, 232001, Anhui, People’s Republic of China

    Yu Su

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  1. Yu Su
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Su, Y. Fractional p-Laplacian Problem with Critical Stein–Weiss Type Term. J Geom Anal 33, 160 (2023). https://doi.org/10.1007/s12220-023-01209-w

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