Solution to biharmonic equation with vanishing potential

Abstract

We establish a result on the existence of nontrivial solution for the following class of biharmonic elliptic equation

\[(\mathrm{P})\quad \Bigl\{\begin{array}{l@{\quad}l}\Delta^{2}u+V(x)u=K(x)f(u)&\mbox{in }R^{N},\\u\neq0,&\mbox{in }R^{N},u\in\mathcal{D}^{2,2}(R^{N}),\end{array}\]

where $\Delta^{2}u=\Delta(\Delta u)$, $V$ and $K$ are nonnegative potentials. $K$ vanishes at infinity and $f$ has a subcritical growth at infinity. The technique used here is the variational approach.