Existence and nonexistence criteria for a system of biharmonic wave inequalities in an exterior domain of ℝN

Abstract

We consider a system of nonlinear biharmonic wave inequalities posed in an exterior domain of [Formula: see text]. Three types of boundary conditions are investigated. For each case, the existence and nonexistence of weak solutions are studied. Our study yields naturally existence and nonexistence results for the corresponding stationary system and equation. Many new results are provided and some open questions are proposed.