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Qualitative properties and classification of solutions to elliptic equations with Stein-Weiss type convolution part

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Abstract

In this paper, we study the qualitative properties and classification of the solutions to the elliptic equations with Stein-Weiss type convolution part. Firstly, we study the qualitative properties, such as the symmetry, regularity and asymptotic behavior of the positive solutions. Secondly, we classify the non-positive solutions by proving some Liouville type theorems for the finite Morse index solutions and stable solutions to the nonlocal elliptic equations with double weights.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 11971436 and 12011530199) and Natural Science Foundation of Zhejiang (Grant No. LD19A010001). The authors are truly grateful to the anonymous referees for their careful reading of the manuscript and suggestions which helped to improve the presentation of the paper greatly.

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, China

    Xiang Li, Minbo Yang & Xianmei Zhou

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  1. Xiang Li
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  2. Minbo Yang
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  3. Xianmei Zhou
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Correspondence to Minbo Yang.

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Li, X., Yang, M. & Zhou, X. Qualitative properties and classification of solutions to elliptic equations with Stein-Weiss type convolution part. Sci. China Math. 65, 2123–2150 (2022). https://doi.org/10.1007/s11425-021-1918-1

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  • DOI: https://doi.org/10.1007/s11425-021-1918-1

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