Gradient estimates for a nonlinear equation under the almost Ricci soliton condition

In this paper, we study the gradient estimate for the positive solutions of the equation \Delta u+au(\log u)^{p}+bu=f on an almost Ricci soliton (M^{n},g,X,\lambda). In a special case, when X=\nabla h for a smooth function h, we derive a gradient estimate for an almost gradient Ricci soliton.

Keywords:

Gradient almost Ricci solitons , Gradient estimates , Almost Ricci solitons