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2022 Multiple solutions for biharmonic critical Choquard equation involving sign-changing weight functions
Anu Rani, Sarika Goyal
Topol. Methods Nonlinear Anal. 59(1): 221-260 (2022). DOI: 10.12775/TMNA.2021.025

Abstract

The purpose of this article is to deal with the following biharmonic critical Choquard equation\begin{align*}\begin{cases}\Delta^{2}u = \lambda f(x) |u|^{q-2}u+ g(x)\bigg(\displaystyle \int_{\Omega}\frac{g(y)|u(y)|^{2_\alpha^*}}{|x-y|^{\alpha}}dy\bigg)|u|^{2_\alpha^*-2}u & \text{in } \Omega,\\u,\ \nabla u = 0 & \text{on } \partial\Omega,\end{cases}\end{align*}where $\Omega$ is a bounded domain in $\mathbb R^N$ with smooth boundary $\partial \Omega$, $N\geq 5$, $1< q < 2$, $0< \alpha < N$, $2_\alpha^*=({2N-\alpha})/({N-4})$ is the critical exponent in the sense of Hardy-Littlewood-Sobolev inequality and $\lambda > 0$ is a parameter. The functions $f, g\colon \overline {\Omega}\rightarrow \mathbb R$ are continuous sign-changing weight functions. Using the Nehari manifold and fibering map analysis, we prove the existence of two nontrivial solutions of the problem with respect to parameter $\lambda$.

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Anu Rani. Sarika Goyal. "Multiple solutions for biharmonic critical Choquard equation involving sign-changing weight functions." Topol. Methods Nonlinear Anal. 59 (1) 221 - 260, 2022. https://doi.org/10.12775/TMNA.2021.025

Information

Published: 2022
First available in Project Euclid: 3 June 2021

Digital Object Identifier: 10.12775/TMNA.2021.025

Keywords: Biharmonic Choquard equation , concave-convex nonlinearities , Critical exponent , Nehari manifold , Sign-changing weight functions

Rights: Copyright © 2022 Juliusz P. Schauder Centre for Nonlinear Studies

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Vol.59 • No. 1 • 2022
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