An application of Kato’s inequality to quasilinear elliptic problems

Let L be a general second order differential elliptic operator. By using a quasilinear version of Kato’s inequality, we prove that the only weak solution of the problem L(u) = |u|^(q−1) u on RN , q > p − 1, is u = 0. Here p ≥ 1 is related to L.