Affiliation:
1. Dipartimento di Matematica e Applicazioni, Università degli Studi “Federico II” di Napoli, via Cinthia, 80126Napoli, Italy
Abstract
AbstractIn this work we study the following fractional scalar field equation:\left\{\begin{aligned} \displaystyle(-\Delta)^{s}u&\displaystyle=g^{\prime}(u)%
\quad\mbox{in }\mathbb{R}^{N},\\
\displaystyle u&\displaystyle>0,\end{aligned}\right.where {N\geq 2}, {s\in(0,1)}, {(-\Delta)^{s}} is the fractional Laplacian and the nonlinearity {g\in C^{2}(\mathbb{R})} is such that {g^{\prime\prime}(0)=0}.
By using variational methods, we prove the existence of a positive solution which is spherically symmetric and decreasing in {r=|x|}.
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