Subelliptic equations with singular nonlinearities on the Heisenberg group

Subelliptic equations with singular nonlinearities on the Heisenberg group

Multiplicity of Solutions of Quasilinear Subelliptic Equations on Heisenberg Group

In this paper, a class of quasilinear elliptic equations on the Heisenberg Group is concerned. Under some suitable assumptions, by virtue of the nonsmooth critical point theory, the existence of infinitely many weak solutions of the problems is obtained. Mathematics Subject Classification: 35J20, 35J25, 65J67

Singular Convolution Operators on the Heisenberg Group

1. Statement of results and outline of method. The purpose of this note is to announce results dealing with convolution operators on the Heisenberg group. As opposed to the well-known situation where the kernels are homogeneous and C°° away from the origin, the kernels we study are homogeneous but have singularities on a hyperplane. Convolution operators with such kernels arise in the study of ...

Degenerate elliptic equations with singular nonlinearities

The behavior of the “minimal branch” is investigated for quasilinear eigenvalue problems involving the p-Laplace operator, considered in a smooth bounded domain of RN , and compactness holds below a critical dimension N #. The nonlinearity f (u) lies in a very general class and the results we present are new even for p = 2. Due to the degeneracy of p-Laplace operator, for p = 2 it is crucial to...

Semi-linear Sub-elliptic Equations on the Heisenberg Group with a Singular Potential

In this work, we study the Dirichlet problem for a class of semi-linear subelliptic equations on the Heisenberg group with a singular potential. The singularity is controlled by Hardy’s inequality, and the nonlinearity is controlled by Sobolev’s inequality. We prove the existence of a nontrivial solution for a homogenous Dirichlet problem.