A note on unique continuation of eigenfunctions for p-Laplacian operator in a bounded domain O in Rn with a potential V in Lp(O)

The aim of this note is to study the problem $ -{\rm div}(|\nabla u|<^>{p-2}\nabla u)+V|u|<^>{p-2}u=0 $ -div(| backward difference u|p-2 backward difference u)+V|u|p-2u=0 in ?, where ? is a bounded domain in $ \mathds {R}<^>n $ Rn and the potential V is assumed to be not equivalent to zero and lies in $ L_p(\Omega ) $ Lp(?). Also, we establish the strong unique continuation property of the eigenfunctions for the p-Laplacian operator in the case where $ V\in L_p(\Omega ) $ V & ISIN;Lp(?).