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arXiv · 1705.05775

Nonlocal Pertubations of Fractional Choquard Equation

Gurpreet Singh
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Abstract

We study the equation \begin{equation} (-Δ)^{s}u+V(x)u= (I_α*|u|^{p})|u|^{p-2}u+λ(I_β*|u|^{q})|u|^{q-2}u \quad\mbox{ in } \R^{N}, \end{equation} where $I_γ(x)=|x|^{-γ}$ for any $γ\in (0,N)$, $p, q >0$, $α,β\in (0,N)$, $N\geq 3$ and $ λ\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.

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Gurpreet Singh. 2017-05-16. Nonlocal Pertubations of Fractional Choquard Equation. https://arxiv.org/abs/1705.05775

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