The Property Analysis Of Solutions For Some Classes Of Singular Elliptic Systems

In this paper, we are concerned with the analysis of solutions for the nonlinear and quasi-linear singular elliptic systems. We will establish Liouville-type theorem for the nonlinear Schr(?)dinger system with Hardy potential by the use of the Kelvin transformation, the test function, the integral estimate and differential equation theory. Besides, we will propose a new comparison principle; and we are able to show that the system does not admit any blow-up nonradial solutions by using the new comparison principle and the radial integral iteration, functional analysis and differential equation theory. This paper is composed of five chapters as follows:· In Chapter 1, we systematically introduce the research background and significance of thesis, and present the domestic and foreign research situation and development trend.· In Chapter 2, we introduce the related preliminaries and lemma in this thesis.· In Chapter 3, we are concerned with Liouville-type theorem for the solution of the nonlinear Schr(?)dinger system with Hardy potential where N?2, ?,??0, p, q > 1,l, n ?(-?, (N-2)2/4). We firstly transform the nonlinear Schr(?)dinger system with Hardy potential into the weighted elliptic system, Then, based on the test function and the integral estimate, we prove Liouville-type theorem of the nonnegative classical solutions; thus, the nonexistence for the solution of the system.· In Chapter 4, we consider the nonexistence for blow-up nonradial solutions of the quasi-linear elliptic system where pi? 2,i?{1,…,m}and ?pi ui=div(|?ui|pi-2?ui),?i and ?i are positive contin-uous functions, fi is non-negative continuous function and non decreasing in each compo-nent ui.Firstly, we establish a new comparison principle, and we are able to show that the system does not admit any blow-up nonradial solutions by using the new comparison principle and the radial integral iteration.· In Chapter 5, we summarize the whole text.