Nonexistence for higher order evolution inequalities with Hardy potential in RN

We study the nonexistence of nontrivial weak solutions to evolution inequalities of the form{∂tku−Δu+λ|x|2u≥|u|pin (0,∞)×RN,∂tiu(0,x)=ui(x),i=0,1,⋯,k−1,in RN, where u=u(t,x), k≥2 is a natural number, ∂ti=∂i∂ti, N≥3, 2k(N−2+2k)≤λ<2N and p>1. Namely, we show that, if uk−1≥0, then for all p>1, there is no nontrivial weak solution. Our result improves a previous result obtained in El Hamidi and Laptev (2005) [5], where the nonexistence of nontrivial weak solution has been established only for a certain range of p.