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

Mousomi Bhakta, Debangana Mukherjee

DOI: http://dx.doi.org/10.12775/TMNA.2017.052

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, $N> ps$.

Keywords


p-fractional; nonlocal; concave-convex; critical; sign-changing; Nehari manifold

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