1 citations · 1 across the 13 of their papers we have counts for
15 papers
Classification of global solutions to the singular equation in a Lipschitz epigraphical cone
Yahong Guo, Congming Li, Chilin Zhang
We construct and classify all global solutions to the singular equation supported in a general Lipschitz epigraphical cone, where is a locally Dini…
Liouville Theorems for the Lane-Emden Equation Involving a Mixed Local-Nonlocal Operator
Yahong Guo, Congming Li, Jiongduo Xie
In this paper, we investigate the existence of positive supersolutions for the following mixed local-nonlocal Lane-Emden type equation: $$ -Δu+(-Δ)^s u=u^q\quad\text{in }\mathbb R^…
Classification of solutions to a weighted singular fractional problem in the half space
Yahong Guo, Chilin Zhang
We focus on the classification of positive solutions to in the half space with , subject to the Dirichlet condition. We show that when $-2s<α<(γ-1…
A convergence result for the master operator
Wenxiong Chen, Yahong Guo, Congming Li +1
In this paper, we establish a convergence result for the fully fractional heat operator $\ma{s}$, also known as the master operator, stated as follows: \[\mbox{If\ }u_i\to u\ \mbox…
Monotonicity for the fractional semi-linear problem in a half space
Wenxiong Chen, Yahong Guo, Leyun Wu
In this paper, we study semilinear fractional equations in a half-space and prove that all positive solutions are strictly increasing in the -directi…
Pointwise regularity of solutions for fully fractional parabolic equations
Yahong Guo, Qizhen Shen, Jiongduo Xie
This paper investigates the higher pointwise regularity of nonnegative classical solutions for fully fractional parabolic equations where .…
Methods in studying qualitative properties of fractional equations
Wenxiong Chen, Yahong Guo, Congming Li
In this paper, we systematically review a series of effective methods for studying the qualitative properties of solutions to fractional equations. Beginning with the pioneering ex…
Boundary regularity and a priori estimates for fractional equations on unbounded domains
Yahong Guo, Congming Li, Yugao Ouyang
In this paper, we study the boundary Hölder regularity for solutions to the fractional Dirichlet problem in unbounded domains with boundary \begin{equation*} \begin{cases} (-Δ)^s u…
Boundary regularity theory of the singular Lane-Emden-Fowler equation in a Lipschitz domain
Yahong Guo, Congming Li, Chilin Zhang
We study the singular Lane-Emden-Fowler equation \begin{equation} -Δu=f(X)\cdot u^{-γ} \end{equation} in a bounded Lipschitz domain , with the Dirichlet boundary condition and a…
Regularity of solutions for fully fractional parabolic equations
Wenxiong Chen, Yahong Guo, Congming Li
In this paper, we study the fully fractional heat equation involving the master operator: $$ (\partial_t -Δ)^{s} u(x,t) = f(x,t)\ \ \mbox{in}\ \mathbb{R}^n\times\mathbb{R} , $$ whe…
Liouville type theorems for dual nonlocal evolution equations involving Marchaud derivatives
Yahong Guo, Lingwei Ma, Zhenqiu Zhang
In this paper, we establish a Liouville type theorem for the homogeneous dual fractional parabolic equation \begin{equation} \partial^α_t u(x,t)+(-Δ)^s u(x,t) = 0\ \ \mbox{in}\ \ \…
Master equations with indefinite nonlinearities
Wenxiong Chen, Yahong Guo
In this paper, we consider the following indefinite fully fractional heat equation involving the master operator \begin{equation} (\partial_t -Δ)^{s} u(x,t) = x_1u^p(x,t)\ \ \mbox{…
A Liouville Theorem and Radial Symmetry for dual fractional parabolic equations
Yahong Guo, Lingwei Ma, Zhenqiu Zhang
In this paper, we first study the dual fractional parabolic equation \begin{equation*} \partial^α_t u(x,t)+(-Δ)^s u(x,t) = f(u(x,t))\ \ \mbox{in}\ \ B_1(0)\times\R , \end{equation*…
Liouville theorem for fully fractional master equations and its applications
Wenxiong Chen, Lingwei Ma, Yahong Guo
In this paper, we study the fully fractional master equation \begin{equation}\label{pdeq1} (\partial_t-Δ)^s u(x,t) =f(x,t,u(x,t)),\,\,(x, t)\in \mathbb{R}^n\times \mathbb{R}. \end{…
Radial symmetry and Liouville theorem for master equations
Lingwei Ma, Yahong Guo, Zhenqiu Zhang
This paper has two primary objectives. The first one is to demonstrate that the solutions of master equation \begin{equation*} (\partial_t-Δ)^s u(x,t) =f(u(x, t)), \,\,(x, t)\in B_…