Author

Zheng-Ce Zhang

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Preprint Sep 2026

Liouville-type theorems and universal estimates for semilinear elliptic equations involving the product of the function and its gradient

In this paper, we study local and global properties of positive solutions to the equation $-\Delta u=u^p|\nabla u|^q$ in a domain $\Omega$ of $\mathbb R^N$, where $p$ and $q$ are parameters. We introduce a linear operator to construct the differential inequality to obtain gradient estimates, and further establish Liouv...

Wen-Guo Liang, Zheng-Ce Zhang · 1 citation

Preprint Sep 2026

Gradient estimates and Liouville-type theorems for the semilinear elliptic equation involving the nonlinear gradient source

We study local and global properties of positive solutions to the equation $-\Delta u=u^p+M|\nabla u|^q$ in a domain $\Omega$ of $\mathbb R^N$, where $p,q$ are parameters and $M>0$. By constructing a linear operator, we establish the differential inequality containing an auxiliary function. By selecting appropriate aux...

Wen-Guo Liang, Zheng-Ce Zhang · 0 citations