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Nonlocal Pertubations of Fractional Choquard Equation. (arXiv:1705.05775v1 [math.AP])
来源于:arXiv
We study the equation \begin{equation} (-\Delta)^{s}u+V(x)u=
(I_{\alpha}*|u|^{p})|u|^{p-2}u+\lambda(I_{\beta}*|u|^{q})|u|^{q-2}u \quad\mbox{
in } \R^{N}, \end{equation} where $I_\gamma(x)=|x|^{-\gamma}$ for any
$\gamma\in (0,N)$, $p, q >0$, $\alpha,\beta\in (0,N)$, $N\geq 3$ and $ \lambda
\in R$. First, the existence of a groundstate solutions using minimization
method on the associated Nehari manifold is obtained. Next, the existence of
least energy sign-changing solutions is investigated by considering the Nehari
nodal set. 查看全文>>