2021 Sign-changing solutions for the boundary value problem involving the fractional $p$-Laplacian
Pengcheng Wu, Yuying Zhou
Topol. Methods Nonlinear Anal. 57(2): 597-619 (2021). DOI: 10.12775/TMNA.2020.051

Abstract

In the paper, we consider the following boundary value problem involving the fractional $p$-Laplacian: \begin{equation} \tag{$\mathcal{P}$} \begin{cases} (-\triangle)_p^su(x)=f(x,u) &\text{in } \Omega,\\ u(x)=0 &\text{in } \mathbb{R}^N\setminus\Omega. \end{cases} \end{equation} where $\Omega$ is a bounded smooth domain in $\mathbb{R}^N$ with $N\geq 1$, $(-\Delta)_p^{s}$ is the fractional $p$-Laplacian with $s\in (0,1)$, $p\in(1,{N}/{s})$, $f(x, u)\colon \Omega\times\mathbb{R}\rightarrow\mathbb{R}$. Under the improved subcritical polynomial growth condition and other conditions, the existences of a least-energy sign-changing solution for the problem $(\mathcal{P})$ has been established.

Citation

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Pengcheng Wu. Yuying Zhou. "Sign-changing solutions for the boundary value problem involving the fractional $p$-Laplacian." Topol. Methods Nonlinear Anal. 57 (2) 597 - 619, 2021. https://doi.org/10.12775/TMNA.2020.051

Information

Published: 2021
First available in Project Euclid: 4 August 2021

MathSciNet: MR4359728
zbMATH: 1479.35497
Digital Object Identifier: 10.12775/TMNA.2020.051

Rights: Copyright © 2021 Juliusz P. Schauder Centre for Nonlinear Studies

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Vol.57 • No. 2 • 2021
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