Related papers: Liouville theorems for Kirchhoff-type hypoelliptic…
In this paper, we establish Liouville type results for semilinear subelliptic systems associated with the sub-Laplacian on the Heisenberg group $\mathbb{H}^{n}$ involving two different kinds of general nonlinearities. The main technique of…
In this paper, we establish Liouville theorems for the following system of elliptic differential inequalities $$ \Delta_{\mathbb H}u^{m_1}+|\eta|_{\mathbb H}^{\gamma_1}|v|^p\leq0,$$ $$ \Delta_{\mathbb H}v^{m_2}+|\eta|_{\mathbb…
In this paper we obtain a Liouville type theorem to the semilinear subcritical elliptic equation on H-type groups. The semilinear subcritical elliptic equation studied in this paper is a generalization of a classical semilinear subcritical…
This paper studies Liouville properties for viscosity sub- and supersolutions of fully nonlinear degenerate elliptic PDEs, under the main assumption that the operator has a family of generalized subunit vector fields that satisfy the…
We establish a Liouville-type theorem for a subcritical nonlinear problem, involving a fractional power of the sub-Laplacian in the Heisenberg group. To prove our result we will use the local realization of fractional CR covariant…
In this paper, we establish Liouville-type theorems for parabolic differential inequalities with $(p,q)-$Laplacian operator on Riemannian manifolds. By a test function argument, we establish nonexistence results under suitable weighted…
In the present paper we derive Liouville type results and existence of periodic solutions for $\chi^{(2)}$ type systems with non-homogeneous nonlinearities. Moreover, we prove both universal bounds as well as singularity and decay estimates…
We prove new (sharp) Liouville-type properties via degenerate Hadamard three-sphere theorems for fully nonlinear equations structured over Heisenberg vector fields. As model examples, we cover the case of Pucci's extremal operators…
The purpose of this paper is to investigate the non-existence of global weak solutions of the following degenerate inequality on the Heisenberg group $$ \begin{cases} u_{t}-\Delta_{\mathbb{H}}u\geq…
We prove nonexistence results of Liouville type for nonnegative viscosity solutions of some equations involving the fully nonlinear degenerate elliptic operators ${\cal P}^\pm_k$, defined respectively as the sum of the largest and the…
In this paper, existence of solutions is established for critical exponential Kirchhoff systems on the Heisenberg group by using the variational method. The novelty of our paper is that not only the nonlinear term has critical exponential…
We obtain an entire Liouville type theorem to the classical semilinear subcritical elliptic equation on Heisenberg group. A pointwise estimate near the isolated singularity was also proved. The soul of the proofs is an a priori integral…
In this paper, we establish the sharp criteria for the nonexistence of positive solutions to the Hardy-Littlewood-Sobolev (HLS) type system of nonlinear equations and the corresponding nonlinear differential systems of Lane-Emden type…
In \cite{LWZ}, we establish Liouville-type theorems and decay estimates for solutions of a class of high order elliptic equations and systems without the boundedness assumptions on the solutions. In this paper, we continue our work in…
We establish Liouville type theorems in the whole space and in a half-space for parabolic problems without scale invariance. To this end, we employ two methods, respectively based on the corresponding elliptic Liouville type theorems and…
We provide a simple method for obtaining new Liouville theorems for scaling invariant superlinear parabolic problems with gradient structure. To illustrate the method we prove Liouville theorems (guaranteeing nonexistence of positive…
This article presents a comprehensive study of \textit{Kirchhoff-type Critical Elliptic Equations} involving $p$-sub-Laplacian Operators on the \textit{Heisenberg Group} $\mathcal{H}_{n}$. It delves into the mathematical framework of…
Motivated by recent interest on Kirchhoff-type equations, in this short note we utilize a classical, yet very powerful, tool of nonlinear functional analysis in order to investigate the existence of positive eigenvalues of systems of…
In this note, we prove two Liouville theorems for fully nonlinear uniformly elliptic equations on half spaces. The main tools are the boundary pointwise regularity, the Hopf type estimate and the Carleson type estimate. Our new proof is…
In this paper, we establish several Liouville type theorems for entire solutions to fractional parabolic equations. We first obtain the key ingredients needed in the proof of Liouville theorems, such as narrow region principles and maximum…