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

Hajiaghasi, Sakineh; Azami, Shahroud

doi:10.22034/cmde.2024.56129.2344

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

Document Type : Research Paper

Authors

Sakineh Hajiaghasi ¹
Shahroud Azami ²

¹ Department of Pure Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, Iran.

² Department of pure Mathematics, Faculty of Sciences Imam Khomeini International University, Qazvin, Iran.

10.22034/cmde.2024.56129.2344

Abstract

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.

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Main Subjects