Liouville Type Results For Polyharmonic Inequalities with Nonlocal Terms

In this note, we study the polyharmonic inequalities system(−∆)mui≥n∑j=1eij(Ψij(|x|)∗upijj)uqijiinN, i= 1,2,···,n,(0.1)whereN≥1 andm≥1 are integers,pij≥1,qij>0. ∆mdenotes the m-polyharmonic operator. Theoperator∗denotes the convolution and Ψijis a function that has certain properties. (eij) is the adjacencymatrix. By poly-superharmonic propery of u and some estimates, we get a Liouville type result of (0.1),which generalize the recent results on these inequalities.