Classification of finite energy solutions to the fractional Lane-Emden-Fowler equations with slightly subcritical exponents
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Date
2017
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Abstract
We study qualitative properties of solutions to the fractional Lane-Emden-Fowler equations with slightly subcritical exponents where the associated fractional Laplacian is defined in terms of either the spectra of the Dirichlet Laplacian or the integral representation. As a consequence, we classify the asymptotic behavior of all finite energy solutions. Our method also provides a simple and unified approach to deal with the classical (local) Lane-Emden-Fowler equation for any dimension >2.
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Keywords
Fractional Laplacian, Critical nonlinearity, Multi-peak solutions, Blow-up analysis