  We study some basic properties of generalized Morrey spaces
$\mathcal{M}^{p,\phi}(\R^{d})$. Also, the problem $-\mbox{div}(|\nabla
u|^{p-2}\nabla u)+V|u|^{p-2}u=0$ in $\Omega$, where $\Omega$ is a bounded open
set in $\R^d$, and potential $V$ is assumed to be not equivalent to zero and
lies in $\mathcal{M}^{p,\phi}(\Omega)$, is studied. Finally, we establish the
strong unique continuation for the $p$-Laplace operator in the case
$V\in\mathcal{M}^{p,\phi}(\R^d)$.
