Multiple solutions for polyharmonic equations with potential vanishing
at infinity
Abstract
We are concerned with the following polyharmonic equation:
\begin{equation*} \Delta_p^L
u+V(x)|u|^{p-2}u = K(x)f(x,u) and
u>0 in \Bbb R^N,
\end{equation*} where $1<
p<\infty$, $N>Lp$,
$L=1,2,\cdots$ and the potential functions $V,
K:\Bbb
R^{N}\to(0,\infty)$ are continuous.
We study the existence and multiplicity of nontrivial positive weak
solutions for the problem above via mountain pass theorem and fountain
theorem.