Abstract
In this paper we consider the following supercritical biharmonic problem:
$$
\begin{cases}
\Delta^2 u= K(x)u^{p+\epsilon}&\text{in } \Omega,\\
u> 0 &\text{in }\Omega,\\
u=\Delta u=0&\text{on }\partial\Omega,
\end{cases}
$$
where $K(x)\in C^3(\overline{\Omega})$ is a nonnegative function,
$p=({N+4})/({N-4})$, $\epsilon> 0$, $\Omega$ is a smooth bounded domain
in $\mathbb{R}^N$, $N\geq6$. We show that, for $\epsilon$ small enough,
there exists a family of concentrating solutions under certain assumptions
on the critical points of the function $K(x)$.
Publisher
Uniwersytet Mikolaja Kopernika/Nicolaus Copernicus University