Existence And Multiplicity Of Solutions To The Elliptic Equations Systems On The Heisenberg Group

With the rapid development and continuous accumulation of differential equations,a variety of nonlinear differential equation problems have been widely concerned and studied by scholars at home and abroad.The problems on Heisenberg group are very new and have important applications in the fields of partial differential equations and number theory.In this paper,we are interested in the existence and multiplicity of solutions for the following elliptic equations on the Heisenberg group.The paper is organized the following four main chapters.In chapter 1,we give some necessary preliminary knowledge,research results and research significance on the Heisenberg group.In chapter 2,we study a class of Schr(?)dinger-Poisson equations with noncooperative critical terms on Heisenberg groups.By using the concentrated compactness lemma to deal with the problem of missing compactness conditions,and combining the Limit index to deal with non-cooperative critical terms,we obtain the existence and multiplicity of solutions.In chapter 3,the degenerate Kirchhoff equations with critical terms on Heisenberg group are studied.The Kirchhoff functions in the equations contain degenerate cases.The existence and multiplicity of the solutions of the equations are proved by combining the mountain road theorem and the concentrated compactness principle.In chapter 4,we discuss the Kirchhoff equations with critical exponential growth on Heisenberg group.The nonlinear terms of the equations have critical exponential growth and the Kirchhoff function contains degradation.The existence and multiplicity of the solutions to the Heisenberg group are proved by the variational method.