Acta mathematica scientia,Series A ›› 2000, Vol. 20 ›› Issue (4): 474-479.
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Abstract:
Let (Mn, g) be a complete Riemannian manifold of dimention n with Ricci curvature RicM(x)≥-A(1+r2(x)ln2(2+r(x))), where A is a nonnegative constant and r(x) is the geodesic distance from x to some fixed point x0∈M.\$ In this paper, we show that there is no nonnegative C2 solution but zero to the equation Δu+Su+Kuα=0 on M under such conditions as: S≤0 on M; K<0 on M and K≤-a2<0 outside some compact set for a constant a>0 and any constant α>1.
Key words: Riemannian manifold, Ricci curvature, Elliptic equation, Liouville theorem.
CLC Number:
Hu Zejun. A Liouville Theorem for a Class of Nonlinear Elliptic Equations[J].Acta mathematica scientia,Series A, 2000, 20(4): 474-479.
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http://121.43.60.238/sxwlxbA/EN/Y2000/V20/I4/474
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