Gradient estimates for some elliptic equation

In this paper, we obtain the gradient estimates of the positive solutions to the following equation defined on an n-dimensional complete Riemannian manifold \Delta _gu+au^q\left(\mathrml\mathrmn\;u\right)^p+bu=0 ． The gradient bound does not depend on the bounds of the solution and the Laplacian of the distance function． Our result is an extension of the estimates on positive harmonic function 1 and the estimates of solutions to some nonlinear elliptic equation 10．