Existence of Solutions for p(x)-Triharmonic Problem with Navier Boundary Conditions

In this paper, we use the Mountain pass theorem and the Fountain theorem to study the existence of solutions for the following p(x)-triharmonic equations: $$\begin{aligned} {\left\{ \begin{array}{ll} -\Delta _{p(x)}^{3} u=\lambda f(x,u), & \hbox { in } \Omega,\\ u=\Delta u=\Delta ^{2}u=0, & \hbox { on }\partial \Omega.\\ \end{array}\right. } \end{aligned}$$