Hopf Type H-type Group, The Strong Maximum Principle And Liouville Type Theorem

This paper is devoted to the study of some Liouville type theorems for the sub-Laplace equations and p -sub-Laplace equations on groups of Heisenberg type.In Chapter 1, some basic definitions and results on groups of Heisenberg type are given. We also describe the problems and background studied in this paper.Chapter 2 gives some Liouville type theorems of sub-Laplace equationsLu + h(ζ)u^a ≤ 0 on unbounded domains and the whole space by means of priorestimate.In Chapter 3, we establish some Hopf type principles and some strong maximumprinciples concerning p -sub-Laplacian on groups of Heisenberg type. Then some Liouville type results for p -sub-Laplace equations are obtained.