Multiple positive bound state solutions for a critical Choquard equation
نویسندگان
چکیده
In this paper we consider the problem style='text-indent:20px;'> \begin{document}$ (P_{\lambda})\ \ \left\{ \begin{array}{rcl} -\Delta u+V_{\lambda}(x)u = (I_{\mu}*|u|^{2^{*}_{\mu}})|u|^{2^{*}_{\mu}-2}u \mbox{in} \mathbb{R}^{N}, \\ u>0 \end{array} \right. $\end{document} style='text-indent:20px;'>where \begin{document}$ V_{\lambda} \lambda+V_{0} $\end{document} with id="M2">\begin{document}$ \lambda \geq 0 $\end{document}, id="M3">\begin{document}$ V_0\in L^{N/2}({\mathbb{R}}^N) id="M4">\begin{document}$ I_{\mu} \frac{1}{|x|^\mu} is Riesz potential id="M5">\begin{document}$ 0<\mu<\min\{N, 4\} and id="M6">\begin{document}$ 2^{*}_{\mu} \frac{2N-\mu}{N-2} id="M7">\begin{document}$ N\geq 3 $\end{document}. Under some smallness assumption on id="M8">\begin{document}$ V_0 id="M9">\begin{document}$ prove existence of two positive solutions id="M10">\begin{document}$ (P_\lambda) In order to main results, used variational methods combined degree theory.
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ژورنال
عنوان ژورنال: Discrete and Continuous Dynamical Systems
سال: 2021
ISSN: ['1553-5231', '1078-0947']
DOI: https://doi.org/10.3934/dcds.2021061