Research Communication | Open Access
Volume 2019 | Communication ID 36
Volume 2019 | Communication ID 36
| Existence of solutions for a nonlocal Kirchhoff type problem in fractional Orlicz-Sobolev spaces |
Elhoussine Azroul, Abdelmoujib Benkirane, Mohammed Srati
Received |
Accepted |
Published |
Jan 02, 2019 |
Jan 31, 2019 |
Mar 01, 2019 |
Abstract: In this paper, we investigate the existence of weak solution for a Kirchhoff type problem driven by a nonlocal operator of elliptic type in a fractional Orlicz-Sobolev space, with homogeneous Dirichlet boundary conditions {\small$$ (D_{K,A}) \hspace*{0.5cm} \left\{ \begin{array}{clclc} M\left( \displaystyle \int_{\R^{2N}}A\left( [u(x)-u(y)] K(x,y)\right) dxdy\right) \mathcal{L}^K_A u & = & f(x,u) & \text{ in }& \Omega, \\\\ \hspace*{7cm} u & = & 0 \hspace*{0.2cm} \hspace*{0.2cm} & \text{ in } & \R^N\smallsetminus \Omega. \label{eq1} \end{array} \right. $$ ...