7 papers
Multiple sign-changing solutions for semilinear subelliptic Dirichlet problem
Hua Chen, Hong-Ge Chen, Jin-Ning Li +1
We study the following perturbation from symmetry problem for the semilinear subelliptic equation \[ \left\{ \begin{array}{cc} -\triangle_{X} u=f(x,u)+g(x,u) & \mbox{in}~Ω, \\[2mm]…
Critical Sobolev inequalities and global extremals for homogeneous Hörmander vector fields on
Hua Chen, Hong-Ge Chen, Jin-Ning Li
We study critical Sobolev inequalities and Sobolev extremal functions for homogeneous Hörmander vector fields on . The focus is the non-equiregular case. In this setti…
Sharp embedding results and geometric inequalities for Hörmander vector fields
Hua Chen, Hong-Ge Chen, Jin-Ning Li
Let be a connected open subset of , and let be a system of Hörmander vector fields defined on . This paper addresses sharp embedding…
Multiplicity of solutions for semilinear subelliptic Dirichlet problem
Hua Chen, Hong-Ge Chen, Jin-Ning Li +1
In this paper, we study the semilinear subelliptic equation \[ \left\{ \begin{array}{cc} -\triangle_{X} u=f(x,u)+g(x,u) & \mbox{in}~Ω, \\[2mm] u=0\hfill & \mbox{on}~\partialΩ, \end…
Existence and multiplicity of solutions to Dirichlet problem for semilinear subelliptic equation with a free perturbation
Hua Chen, Hong-Ge Chen, Xin-Rui Yuan
This paper is concerned with existence and multiplicity results for the semilinear subelliptic equation with free perturbation term. By using the degenerate Rellich-Kondrachov comp…
Asymptotic behaviour of Dirichlet eigenvalues for homogeneous Hörmander operators and algebraic geometry approach
Hua Chen, Hong-Ge Chen, Jin-Ning Li
We study the Dirichlet eigenvalue problem of homogeneous Hörmander operators on a bounded open domain containing the origin, where $X_1, X_2…
Estimates of Dirichlet Eigenvalues for a Class of Sub-elliptic Operators
Hua Chen, Hongge Chen
Let be a bounded connected open subset in with smooth boundary . Suppose that we have a system of real smooth vector fields $\cdots,…