Let M be an n-dimensional complete noncompact Riemannian manifold with sectional curvature bounded from below, dμ = e^h（x） dV（x） the weighted measure and △μ,p the weighted p-Laplacian. In this paper we consider...Let M be an n-dimensional complete noncompact Riemannian manifold with sectional curvature bounded from below, dμ = e^h（x） dV（x） the weighted measure and △μ,p the weighted p-Laplacian. In this paper we consider the non-linear elliptic equation △μ,pu=-λμ,p｜u｜^p-2ufor p ∈ （1, 2）. We derive a sharp gradient estimate for positive smooth solutions of this equation. As applications, we get a Harnack inequality and a Liouville type theorem..展开更多
Pishu ( BL 20), Dachangshu ( BL 25), Zusanli (ST 36), and Shangjuxu (ST 37) were selected to treat chronic ulcerative colonitis in 43 cases by point injection with placental tissue fluid and the curative effect was co...Pishu ( BL 20), Dachangshu ( BL 25), Zusanli (ST 36), and Shangjuxu (ST 37) were selected to treat chronic ulcerative colonitis in 43 cases by point injection with placental tissue fluid and the curative effect was compared with that of west medicine plus enema in 22 cases (control group). It showed that there was a significant difference in short-term total effective rate between the two groups. It suggested that point therapy was effective.展开更多
基金Supported by the National Natural Science Foundation of China (11171254, 11271209)
文摘Let M be an n-dimensional complete noncompact Riemannian manifold with sectional curvature bounded from below, dμ = e^h（x） dV（x） the weighted measure and △μ,p the weighted p-Laplacian. In this paper we consider the non-linear elliptic equation △μ,pu=-λμ,p｜u｜^p-2ufor p ∈ （1, 2）. We derive a sharp gradient estimate for positive smooth solutions of this equation. As applications, we get a Harnack inequality and a Liouville type theorem..
文摘Pishu ( BL 20), Dachangshu ( BL 25), Zusanli (ST 36), and Shangjuxu (ST 37) were selected to treat chronic ulcerative colonitis in 43 cases by point injection with placental tissue fluid and the curative effect was compared with that of west medicine plus enema in 22 cases (control group). It showed that there was a significant difference in short-term total effective rate between the two groups. It suggested that point therapy was effective.
