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.

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Multiple Solutions to a Magnetic Nonlinear Choquard Equation

We consider the stationary nonlinear magnetic Choquard equation (−i∇+ A(x))u+ V (x)u = (

متن کامل

Multiple solutions of the quasi relativistic Choquard equation

Articles you may be interested in Multi-peak solution for nonlinear magnetic Choquard type equation Smooth soliton solutions of a new integrable equation by Qiao Optimal solution for the viscous nonlinear dispersive wave equation We prove existence of multiple solutions to the quasirelativistic Choquard equation with a scalar potential. C 2012 American Institute of Physics.

متن کامل

Existence of nontrivial weak solutions for a quasilinear Choquard equation

We are concerned with the following quasilinear Choquard equation: [Formula: see text] where [Formula: see text], [Formula: see text] is the p-Laplacian operator, the potential function [Formula: see text] is continuous and [Formula: see text]. Here, [Formula: see text] is the Riesz potential of order [Formula: see text]. We study the existence of weak solutions for the problem above via the mo...

متن کامل

Existence of positive solutions for a boundary value problem of a nonlinear fractional differential equation

This paper presents conditions for the existence and multiplicity of positive solutions for a boundary value problem of a nonlinear fractional differential equation. We show that it has at least one or two positive solutions. The main tool is Krasnosel'skii fixed point theorem on cone and fixed point index theory.

متن کامل

Multiple positive solutions for second order impulsive differential equation ∗

We investigate the existence of positive solutions to a three-point boundary value problem of second order impulsive differential equation. Our analysis rely on the Avery-Peterson fixed point theorem in a cone. An example is given to illustrate our result.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Discrete and Continuous Dynamical Systems

سال: 2021

ISSN: ['1553-5231', '1078-0947']

DOI: https://doi.org/10.3934/dcds.2021061