$p$-Laplacian operator with potential in generalized Morrey Spaces

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