## Topological Methods in Nonlinear Analysis

### Sign changing solutions of $p$-fractional equations with concave-convex nonlinearities

#### Abstract

We study the existence of sign changing solutions to the following $p$-fractional problem with concave-critical nonlinearities: \begin{alignat*}2 (-\Delta)^s_pu &= \mu |u|^{q-1}u + |u|^{p^*_s-2}u &\quad&\mbox{in }\Omega,\\ u&=0&\quad&\mbox{in } \mathbb{R}^N\setminus\Omega, \end{alignat*} where $s\in(0,1)$ and $p\geq 2$ are fixed parameters, $0< q< p-1$, $\mu\in\mathbb{R}^+$ and $p_s^*={Np}/({N-ps})$. $\Omega$ is an open, bounded domain in $\mathbb{R}^N$ with smooth boundary, $N> ps$.

#### Article information

Source
Topol. Methods Nonlinear Anal., Volume 51, Number 2 (2018), 511-544.

Dates
First available in Project Euclid: 18 January 2018

https://projecteuclid.org/euclid.tmna/1516244427

Digital Object Identifier
doi:10.12775/TMNA.2017.052

Mathematical Reviews number (MathSciNet)
MR3829042

Zentralblatt MATH identifier
06738554

#### Citation

Bhakta, Mousomi; Mukherjee, Debangana. Sign changing solutions of $p$-fractional equations with concave-convex nonlinearities. Topol. Methods Nonlinear Anal. 51 (2018), no. 2, 511--544. doi:10.12775/TMNA.2017.052. https://projecteuclid.org/euclid.tmna/1516244427

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