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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 .…