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Radial sign-changing solution for fractional Schrödinger equation

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  • We study the existence of a radial sign-changing solution for the stationary fractional Schrödinger equation \begin{equation}\nonumber (-\Delta)^\alpha u + u=|u|^{p-1}u,\ x\in \mathbb{R}^N, N\geq 2.~~~~~~~~~~~~~{\rm (FS)} \end{equation} where $\alpha\in (0,1)$ and $p\in(1,2_\alpha^*-1)$, $2_\alpha^*=\frac{2N}{N-2\alpha}$. By using Brouwer degree theory and variational method, we prove that there exists a radial sign-changing solution of (FS).
    Mathematics Subject Classification: 35J20, 35J60.


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