Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Yau Type Gradient Estimates For $\Delta u + au(\log u)^{p}+bu=0$ On
  Riemannian Manifolds   In this paper, we consider the gradient estimates of the positive solutions
to the following equation defined on a complete Riemannian manifold $(M, g)$
$$\Delta u + au(\log u)^{p}+bu=0,$$ where $a, b\in \mathbb{R}$ and $p$ is a
rational number with $p=\frac{k_1}{2k_2+1}\geq2$ where $k_1$ and $k_2$ are
positive integer numbers. we obtain the gradient bound of a positive solution
to the equation which does not depend on the bounds of the solution and the
Laplacian of the distance function on $(M, g)$. Our results can be viewed as a
natural extension of Yau's estimates on positive harmonic function.

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The categories of this paper are: physics
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The categories of this paper are: q-fin
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-ex
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The categories of this paper are: supr-con
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The categories of this paper are: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ph
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The categories of this paper are: econ
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The categories of this paper are: q-bio
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The categories of this paper are: math-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: adap-org
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The categories of this paper are: gr-qc
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The categories of this paper are: bayes-an