Polyharmonic inequalities with nonlocal terms

[摘要] We study the existence and non-existence of classical solutions for inequalities of type +/- Delta(m) u = > (Psi(vertical bar x vertical bar) * u(p)) u(q) in R-N (N >= 1). Here, Delta(m)(m >= 1) is the polyharmonic operator, p, q > 0 and * denotes the convolution operator, where Psi > 0is a continuous non-increasing function. We devise new methods to deduce that solutions of the above inequalities satisfy the poly-superharmonic property. This further allows us to obtain various Liouville type results. Our study is also extended to the case of systems of simultaneous inequalities. (C) 2021 The Author(s). Published by Elsevier Inc.

[发布日期] 2021-09-25

[关键词] Polyharmonic inequalities;Nonlocal terms;Poly-superharmonic property;Liouville type results