mountain pass solution for a p(t)-biharmonic_x000D_ kirchhoff-type equation

چکیده مقاله

in this paper we deal with the existence of weak solution for a p(t)-kirchhoff type problem of the following form\left\{\begin{array}{ll}-\left(a-b \int_{\omega}\frac{1}{p(x)}|\delta u|^{p(x)}\,dx\right)\delta(|\delta u|^{p(x)-2}\delta u)=\lambda |u|^{p(x)-2}u+g(x,u) & \text{ in } \omega,\\u=\delta u=0 & \textrm{ on } \partial\omega.\end{array}\right.using the mountain pass theoem, we establish conditions ensuring the existence result.