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On a Degenerate p-Fractional Kirchhoff Equations Involving Critical Sobolev–Hardy Nonlinearities

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Abstract

In this paper, we study a class of degenerate p-fractional Kirchhoff equations with critical Hardy–Sobolev nonlinearities. By means of the Kajikiya’s new version of the symmetric mountain pass lemma, we obtain the existence of infinitely many solutions which tend to zero under a suitable value of \(\lambda \). The main feature and difficulty of our equations is the fact that the Kirchhoff term M could be zero at zero, that is the equation is degenerate. To our best knowledge, our results are new even in the Laplacian and p-Laplacian cases.

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Acknowledgements

Y. Q. Song was supported by NSFC (no. 11301038), The Natural Science Foundation of Jilin Province (no. 20160101244JC), Research Foundation during the 13th 5-Year Plan Period of Department of Education of Jilin Province, China (JJKH20170648KJ), Natural Science Foundation of Changchun Normal University (No. 2017-09). S. Y. Shi was supported by NSFC Grant (no. 11771177), China Automobile Industry Innovation and Development Joint Fund (no. U1664257), Program for Changbaishan Scholars of Jilin Province, and Program for JLU Science, Technology Innovative Research Team (no. 2017TD-20).

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Authors and Affiliations

  1. Scientific Research Department, Changchun Normal University, Changchun, 130032, Jilin, People’s Republic of China

    Yueqiang Song

  2. School of Mathematics & State Key Laboratory of Automotive Simulation and Control, Jilin University, Changchun, 130012, People’s Republic of China

    Shaoyun Shi

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  1. Yueqiang Song
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  2. Shaoyun Shi
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Correspondence to Shaoyun Shi.

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Song, Y., Shi, S. On a Degenerate p-Fractional Kirchhoff Equations Involving Critical Sobolev–Hardy Nonlinearities. Mediterr. J. Math. 15, 17 (2018). https://doi.org/10.1007/s00009-017-1062-z

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  • DOI: https://doi.org/10.1007/s00009-017-1062-z

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