New class of sixth-order nonhomogeneous p(x)-Kirchhoff problems with sign-changing weight functionsHamdani, Mohamed Karim (Avtor) Chung, Nguyen Thanh (Avtor) Repovš, Dušan (Avtor) variable exponentsKirchhoff type problemsp(x)-triharmonic operatorsign-changing functionsconcave-convex termsEkeland's variational principlemultiple solutionsIn this paper, we prove the existence of multiple solutions for the following sixth-order $p(x)$-Kirchhoff-type problem $$\begin{cases} -M\left( \int\limits_{\it \Omega} \frac{1}{p(x)}|\nabla {\it\Delta} u|^{p(x)}dx\right){\it\Delta}^3_{p(x)} u = \lambda f(x)|u|^{q(x)-2}u + g(x)|u|^{r(x)-2}u + h(x) &\mbox{in}\quad {\it\Omega}, \\ u = {\it\Delta} u = {\it\Delta}^2 u = 0, \quad &\mbox{on}\quad \partial{\it\Omega}, \end{cases}$$ where ${\it\Omega} \subset \mathbb{R}^N$ is a smooth bounded domain, $N>3$, ${\it\Delta}_{p(x)}^3u\,\, : =\,\, \operatorname{div} \Big({\it\Delta}(|\nabla {\it\Delta} u|^{p(x)-2}\nabla {\it\Delta} u)\Big)$ is the $p(x)$-triharmonic operator, $p, q, r \in C(\overline{\it\Omega}), 1 < p ( x ) < \frac{N}{3}$ for all $x \in \overline{\it \Omega}, M(s) = a-bs^\gamma, \;a, b, \gamma > 0, \lambda > 0$, $g \colon {\it\Omega} \times \mathbb{R} \to \mathbb{R}$ is a nonnegative continuous function while $f, h \colon {\it\Omega} \times \mathbb{R} \to \mathbb{R}$ are sign-changing continuous functions in ${\it \Omega}$. To the best of our knowledge, this paper is one of the first contributions to the study of the sixth-order $p(x)$-Kirchhoff type problems with sign changing Kirchhoff functions.20212021-07-19 08:25:41Članek v reviji128541sl