TY - JOUR AU - S. Taarabti AU - Z. El Allali AU - K. Ben Haddouch PY - 2020/06/17 Y2 - 2024/03/29 TI - On $\mathcal{p}(x)$-Kirchhoff-type equation involving $\mathcal{p}(x)$-biharmonic operator via genus theory JF - Ukrains’kyi Matematychnyi Zhurnal JA - Ukr. Mat. Zhurn. VL - 72 IS - 6 SE - Research articles DO - 10.37863/umzh.v72i6.6019 UR - https://umj.imath.kiev.ua/index.php/umj/article/view/6019 AB - UDC 517.9The paper deals with the existence and multiplicity of nontrivial weak solutions for the $p(x)$-Kirchhoff-type problem$$ {-M}\!\left(\displaystyle\int\limits_{\Omega}\frac{1}{p(x)}|\Delta u|^{p(x)}\,dx\right)\!\Delta_{p(x)}^{2} u = f(x,u)\quad \mbox{in}\quad \Omega, $$$$ u = \Delta u = 0\quad  \mbox{on}\quad \partial\Omega.$$By using variational approach and Krasnoselskii's genus theory, we prove the existence and multiplicity of solutions for the $p(x)$-Kirchhoff-type equation.  ER -