Journal of the
Korean Mathematical Society JKMS

In this paper we will be concerned with the problem $$\Delta \left(a(|\Delta u|^p)|\Delta u|^{p-2}\Delta u\right)=f(u)\quad \mbox{in}~~\Omega, \qquad u=\frac{\partial u}{\partial n}=0~~\mbox{on}~~~\partial \Omega,$$ where $\Omega\subset\mathbb{R}^{N}$ is a bounded smooth domain with $1

Keywords: $p$-Biharmonic operator, Adam's inequality, critical exponential growth

MSC numbers: 35J20, 35J30, 35J60, 35B33