A discontinuous semilinear problem involving the fractional Laplacian

  • Sabri BENSID Department of Mathematics, Faculty of Sciences, University of Tlemcen.

Abstract

We study the following fractional problem of the type$$
(P)\left\{\begin{array}{ll} (-\Delta )^s u = f(u) & \quad \mbox{
in }\ \Omega,
\\[0.3cm]u =0 &\quad \mbox{ on }\
\R^n \setminus \Omega,
\end{array}
\right. $$ where $(-\Delta)^s$ is the fractional Laplacian,
$\Omega$ is a smooth bounded domain in $\R^n,$
$f$ is a discontinuous nonlinearity. Under different growth assumptions on $f$, we obtain various existence results via the nonsmooth minimax theorems.

Published
May 29, 2017
How to Cite
BENSID, Sabri. A discontinuous semilinear problem involving the fractional Laplacian. Nonlinear Studies, [S.l.], v. 24, n. 2, p. 377-388, may 2017. ISSN 2153-4373. Available at: <http://nonlinearstudies.com/index.php/nonlinear/article/view/1299>. Date accessed: 19 oct. 2017.