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$$ (D_{ K,A}) \hspace*{ 0.5cm} \left\{ \begin{ array}{ clclc} M\left( \displaystyle \int_{ \R^{ 2N}}A\left( [u(x)-u(y)] K(x,y)\right) dxdy\right) \mathcal{ L}^K_A u & = & f(x,u) & \text{ in }& \Omega, \hspace*{ 7cm} u & = & 0 \hspace*{ 0.2cm} \hspace*{ 0.2cm} & \text{ in } & \R^N\setminus \Omega. \label{ eq1} \end{ array} \right. $$ } Where $\mathcal{ L}^K_A$ is a nonlocal operator with singular kernel $K$ and $A$ is an $N$-function, $\Omega$ is an open bounded subset in $\R^N$ with Lipschitz boundary $\partial \Omega$.
Categories: math.AP