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Multiple Solutions to a Transmission Problem with a Critical Hardy-Sobolev Exponential Source Term

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Abstract

In the paper there are established many results for a transmission problem with critical Hardy-Sobolev exponential source term \(\frac{u^3}{|x|}\) in \({\mathbb {R}}^3\). We obtain that there are at least three weakly nontrivial solutions when a positive coefficient of nonhomogeneous term is enough small using the variational method. Next infinitely many classical solutions are obtained when the coefficient equals to zero. Moreover, a new compactness condition is derived with the help of Brezis-Lieb’s lemma and Mazur’s lemma.

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Acknowledgements

The authors would like to thank the anonymous editors and reviewers for helpful comments and suggestions, which will improve the original version of the paper. This work is supported by the Foundation of Research Project of Guizhou Minzu University (Nos. GZMUZK[2021]YB19, GZMUZK[2021]QN04), the Natural Science Foundation of Guizhou Province (No. Qian Jiao He KY-word[2022]180), and the Innovation Team Project of the Education Department of Guizhou Province (No. Qian Jiao Ji[2023]062).

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  1. School of Data Science and Information Engineering, Guizhou Minzu University, Guiyang, 550025, People’s Republic of China

    Yue Wang

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Y.W. wrote the main manuscript text. All authors reviewed the manuscript.

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Correspondence to Yue Wang.

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Wang, Y. Multiple Solutions to a Transmission Problem with a Critical Hardy-Sobolev Exponential Source Term. Qual. Theory Dyn. Syst. 23, 127 (2024). https://doi.org/10.1007/s12346-024-00985-2

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