A Liouville Type Theorem For Polyharmonic Systems And Integral Equations

In this paper, we proved a Liouville type theorem for polyharmonic systems and integral Equations, this paper includes two chapters,In chapter1, we consider polyharmonic systems where m≥1, N>2m, p,q,k,s≥0. We establish conditions for nonexistence of positive radial solutions to this system.we proved the following theorem.Theorem1.1. Suppose N>2m. p, q, k, ssatisfy(i) p, q>0, pq>1,0≤k≤1,0≤s≤1, Then the polyharmonic system (0.1) has no positive radial solutions.In chapter2,we study the system of integral equations where μ is a real number and satisfy0<μ<N and p,q>0.The main theorem as follows.Theorem2.1. For(i) Suppose but not both equal to then the systems (0.2) has no positive solution (u,v) with(ii) Suppose then the positive solution (u,v) of (0.2) with is of the form where a, d>0and x∈RN...