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Fractional Kirchhoff–Choquard equation involving Schrödinger term and upper critical exponent

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Abstract

In this paper, we consider fractional degenerate and non-degenerate Kirchhoff type Schrödinger–Choquard problems with upper critical exponent, respectively. By studying the solutions of limit problems for above problems and establishing some local and global compactness results, we provide some sufficient conditions under which above problems have at least one or two bounded state solutions. Our main tools adopted in our proof are splitting theorem and linking theorem.

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Acknowledgements

Y. Sang is supported by the Programs for the Cultivation of Young Scientific Research Personnel of Higher Education Institutions in Shanxi Province, the Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi (201802085), the Innovative Research Team of North University of China(TD201901) and Shanxi Scholarship Council of China (2021-107). S. Liang was supported by the Foundation for China Postdoctoral Science Foundation (Grant no. 2019M662220), Scientific research projects for Department of Education of Jilin Province, China (JJKH20210874KJ).

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Authors and Affiliations

  1. School of Science, North University of China, Taiyuan, 030051, People’s Republic of China

    Yanbin Sang

  2. College of Mathematics, Changchun Normal University, Changchun, 130032, People’s Republic of China

    Sihua Liang

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  1. Yanbin Sang
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  2. Sihua Liang
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Correspondence to Yanbin Sang.

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Sang, Y., Liang, S. Fractional Kirchhoff–Choquard equation involving Schrödinger term and upper critical exponent. J Geom Anal 32, 5 (2022). https://doi.org/10.1007/s12220-021-00747-5

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  • DOI: https://doi.org/10.1007/s12220-021-00747-5

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