arXiv subjects

Yadong Zheng

Publications and source records attributed to Yadong Zheng.

3 recordsLinked to original sources

arXiv2022

A priori estimates and Liouville type results for quasilinear elliptic equations involving gradient terms

In this article we study local and global properties of positive solutions of $-Δ_mu=|u|^{p-1}u+M|\nabla u|^q$ in a domain $Ω$ of $\mathbb R^N$, with $m>1$, $p,q>0$ and $M\in\mathbb R$. Following some ideas used in \cite{BV,Vron1}, and by using a direct Bernstein method combined with Keller-Osserman's estimate, we obtain several a priori estimates as well as Liouville type theorems. Moreover, we prove a local Harnack inequality with the help of Serrin's classical results.

math.AP↗

arXiv2022

On positive solutions of biharmonic elliptic inequalities on Riemannian manifolds

We investigate the non-existence and existence of positive solutions to biharmonic elliptic inequalities on manifolds. Using Green function and volume growth conditions, we establish the critical exponent for biharmonic problem.

math.AP↗

arXiv2021

Liouville theorems to system of elliptic differential inequalities on the Heisenberg group

In this paper, we establish Liouville theorems for the following system of elliptic differential inequalities $$ Δ_{\mathbb H}u^{m_1}+|η|_{\mathbb H}^{γ_1}|v|^p\leq0,$$ $$ Δ_{\mathbb H}v^{m_2}+|η|_{\mathbb H}^{γ_2}|u|^q\leq0,$$ on different unbounded open domains of Heisenberg group $\mathbb H$, including the whole space, and half space of $\mathbb H$. Here $p>m_2>0$, $q>m_1>0$.

math.AP↗