Abstract
In this article, we will prove the existence of infinitely many positive weak solutions to the following nonlocal elliptic PDE.
where \(\Omega \) is an open bounded domain in \(\mathbb {R}^N\) with Lipschitz boundary, \(N>2s\), \(s\in (0,1)\), \(\gamma \in (0,1)\). We will employ variational techniques to show the existence of infinitely many weak solutions of the above problem.
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Acknowledgements
The author S. Ghosh, thanks the Council of Scientific and Industrial Research (C.S.I.R. Grant No. 09/983(0013)/2017-EMR-I), India, for the financial assistantship received to carry out this research work. Both the authors thanks the research facilities received from the Department of Mathematics, National Institute of Technology Rourkela, India. The authors thank the anonymous reviewers for their constructive comments and suggestions.
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Ghosh, S., Choudhuri, D. Existence of infinitely many solutions for a nonlocal elliptic PDE involving singularity. Positivity 24, 463–479 (2020). https://doi.org/10.1007/s11117-019-00690-4
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DOI: https://doi.org/10.1007/s11117-019-00690-4