Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2018; 55(6): 1869-1889

Online first article July 19, 2018      Printed November 1, 2018

https://doi.org/10.4134/BKMS.b171131

Copyright © The Korean Mathematical Society.

On discontinuous elliptic problems involving the fractional $p$-Laplacian in $\mathbb R^{N}$

In Hyoun Kim, Yun-Ho Kim, Kisoeb Park

Incheon National University, Sangmyung University, Incheon National University

Abstract

We are concerned with the following fractional $p$-Laplacian inclusion: \begin{equation*} (-\Delta)_p^su+V(x)|u|^{p-2}u\in \lambda[\underline{f}(x,u(x)),\, \overline{f}(x,u(x))] \quad \rm{in} \ \ \mathbb R^{N}, \end{equation*} where $(-\Delta)_p^s$ is the fractional $p$-Laplacian operator, $0

Keywords: fractional $p$-Laplacian, weak solution, critical point, degree theory

MSC numbers: 35R11, 35J60, 47H11