Nonlinear Kato class and unique continuation of eigenfunctions for p-Laplacian operator

We study some basic properties of nonlinear kato class m p (n) and m p (n),respectively,for 1 < p < n. also,we study the problem - d i v (|u | p - 2 u) + v | u | p - 2 u = 0 in ω,where ω is a bounded domain in n and the weight function v is assumed to be not equivalent to zero and lies in m p (ω),in the case where p < n. finally,we establish the strong unique continuation property of the eigenfunction for the p -laplacian operator in the case where v m p (ω). © 2013 rené erlín castillo and julio c. ramos fernández.