Nonexistence Of Positive Radial Solutions Of Polyharmonic Systems

In this paper, we consider polyharmonic system where m≥1.N>2m,p,q≥0, and a,b are given nonnegative functions.we establish conditions for nonexistence of positive radial solutions to this system.we proved the following two theorems.Theorem1.1Suppose that N>2m, and α,β, p, q satisfy then the polyharmonic system has no positive radial solutions.Theorem1.2Suppose that N>2m,, p. q>1, and a, b satisfy,(i) a,b∈C[0,∞)∩C1(0,+oo),and a(r),b(r)>O,for r>0,(ii)(a(γ)γδ)’,(b(γ)γδ)’≥>0,γ>0, where then the polyharmonic system (1.1) has no positive radial solutions.This paper includes three chapters.In chapter l,we present a simple research summary of nonexistence of positive radial solutions of polyharmonic systems, list the main theorems in this paper, Theorem1.1and Theorem1.2.In chapter2,we present the process proved of Theorem1.1.In chapter3,we present the process proved of Theorem1.2.