On the Critical Exponents of Certain Nonlinear Boundary-Value Problems with Biharmonic Operator in the Exterior of a Ball

We establish sufficient conditions for the absence of global solutions of the differential inequality $\Delta^2u\geqslant|u|^q$ in the exterior of a ball. We consider various boundary conditions and show that the critical exponents depend on these conditions. The proofs are based on the test function method developed by Mitidieri and Pokhozhaev.