We prove the existence of multiple solutions for following sixth-order $p(x)$-Kirchhoff-type problem: $-M(\int_\Omega \frac{1}{p(x)}|\nabla \Delta u|^{p(x)}dx)\Delta^3_{p(x)} u = \lambda f(x)|u|^{q(x)-2}u + g(x)|u|^{r(x)-2}u h(x) \ \mbox{on} \Omega$ and $ u=\Delta u=\Delta^2 u=0 \partial\Omega,$ where $\Omega \subset \mathbb{R}^N$ is a smooth bounded domain, $N > 3$, $\Delta_{p(x)}^3u \operator...

Mechanics is a fascinating field of physics. Its main purpose is to study the interaction of particles in the presence of forces such as gravity. In contrast to the dynamics of particles, the study of continuous media, such as elastic bodies, is challenging and still today not entirely well-understood. This is due to the fact that continuous media behave in numerous and complex ways. For exampl...