3 papers
math.AP2023
Liouville type theorems for subelliptic systems on the Heisenberg group with general nonlinearity
Rong Zhang, Vishvesh Kumar, Michael Ruzhansky
In this paper, we establish Liouville type results for semilinear subelliptic systems associated with the sub-Laplacian on the Heisenberg group involving two diffe…
math.AP2022
A Direct Method of Moving Planes for Logarithmic Schrödinger Operator
Rong Zhang, Vishvesh Kumar, Michael Ruzhansky
In this paper, we study the radial symmetry and monotonicity of nonnegative solutions to nonlinear equations involving the logarithmic Schrdinger operator $(\mathc…
math.AP2022
Symmetry of positive solutions for Lane-Emden systems involving the Logarithmic Laplacian
Rong Zhang, Vishvesh Kumar, Michael Ruzhansky
We study the Lane-Emden system involving the logarithmic Laplacian: $$ \begin{cases} \ \mathcal{L}_Δu(x)=v^{p}(x) ,& x\in\mathbb{R}^{n},\\ \ \mathcal{L}_Δv(x)=u^{q}(x) ,& x\in\math…