Nonexistence of Global Solutions of Higher Order Evolution Inequalities in R N

Abstract

This paper is devoted to the study of the nonexistence of global nontrivial weak solutions of higher order evolution inequalities in RNof the form: where we assume that m andkare integers greater or equal to 1,q >1 anda <2m. The idea is to find a set of conditions which imply the nonexistence of global weak solutions and to see how this set depends on the order of the operator. In particular, we will define an exponentq*such that ifq < q*, then (1)—(2) does not admit any nontrivial solution in a weak sense to be specified later, (see Definition 2.1). We will address toq*as to thecritical exponentof problem (1)—(2)