Abstract
We consider the nonlocal Hénon equation
where \((-\Delta )^s\) is the fractional Laplacian operator with \(0<s<1\), \(-2s<\alpha \), \(p>1\) and \(N>2s\). We prove a nonexistence result for positive solutions in the optimal range of the nonlinearity, that is, when
Moreover, we prove that a bubble solution, that is a fast decay positive radially symmetric solution, exists when \(p=p_{\alpha , s}^{*}\).
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Acknowledgements
B. B. was partially supported by AEI Grant MTM2016-80474-P and Ramón y Cajal fellowship RYC2018-026098-I (Spain). A. Q. was partially supported by Fondecyt Grant No. 1190282 and Programa Basal, CMM. U. de Chile
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Barrios, B., Quaas, A. The sharp exponent in the study of the nonlocal Hénon equation in \({\mathbb {R}}^{N}\): a Liouville theorem and an existence result. Calc. Var. 59, 114 (2020). https://doi.org/10.1007/s00526-020-01763-z
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DOI: https://doi.org/10.1007/s00526-020-01763-z