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 $1 Lp$, $L=1,2,\cdots$ 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.
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