The Existence And Non-existence Of Linear Elliptic Equations (group) Proposed Two Types Of Positive Solutions

In this paper, we investigate the existence and nonexistence of the solutions for two kinds of quasilinear elliptic equation or system.In chapter1, we consider the equation△mu=p(x)uα+q(x)uβ,0<α≤β.(0.0.3) where p, q are nonnegative continuous functions and0<α≤β. We con-sider the existence and nonexistence results of explosive solutions for β> m-1(superlinear/mixed case), and the existence results both for explosive solution and bounded solution for β≤m-1(sublinear case).In chapter2, the existence of entire solutions for the following quasilinear elliptic systems are considered, wheref, g are continuous and non-decreasing on [0,∞), satisfying the Keller-Osserman condition. We establish conditions on p and q which are necessary for the positive solutions to be bounded or unbounded.