The semirelativistic Choquard equation with a local nonlinear term
B Bieganowski, S Secchi - arXiv preprint arXiv:1805.05628, 2018 - arxiv.org
arXiv preprint arXiv:1805.05628, 2018•arxiv.org
We propose an existence result for the semirelativistic Choquard equation with a local
nonlinearity in $\mathbb {R}^ N $\begin {equation*}\sqrt {\strut-\Delta+ m^ 2} u-mu+ V (x)
u=\left (\int_ {\mathbb {R}^ N}\frac {| u (y)|^ p}{| xy|^{N-\alpha}}\, dy\right)| u|^{p-2} u-\Gamma
(x)| u|^{q-2} u,\end {equation*} where $ m> 0$ and the potential $ V $ is decomposed as the
sum of a $\mathbb {Z}^ N $-periodic term and of a bounded term that decays at infinity. The
result is proved by variational methods applied to an auxiliary problem in the half-space …
nonlinearity in $\mathbb {R}^ N $\begin {equation*}\sqrt {\strut-\Delta+ m^ 2} u-mu+ V (x)
u=\left (\int_ {\mathbb {R}^ N}\frac {| u (y)|^ p}{| xy|^{N-\alpha}}\, dy\right)| u|^{p-2} u-\Gamma
(x)| u|^{q-2} u,\end {equation*} where $ m> 0$ and the potential $ V $ is decomposed as the
sum of a $\mathbb {Z}^ N $-periodic term and of a bounded term that decays at infinity. The
result is proved by variational methods applied to an auxiliary problem in the half-space …
We propose an existence result for the semirelativistic Choquard equation with a local nonlinearity in \begin{equation*} \sqrt{\strut -\Delta + m^2} u - mu + V(x)u = \left( \int_{\mathbb{R}^N} \frac{|u(y)|^p}{|x-y|^{N-\alpha}} \, dy \right) |u|^{p-2}u - \Gamma (x) |u|^{q-2}u, \end{equation*} where and the potential is decomposed as the sum of a -periodic term and of a bounded term that decays at infinity. The result is proved by variational methods applied to an auxiliary problem in the half-space .
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