On $\mathcal{p}(x)$-Kirchhoff-type equation involving $\mathcal{p}(x)$-biharmonic operator via genus theory

• Date: 2020
• Main Authors: Taarabti, S., El Allali , Z., Ben Haddouch, K.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2020
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/6019
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

UDC 517.9 The 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,&n...