On the nonexistence of solutions of some anisotropic elliptic and backward parabolic inequalities

We study the nonexistence of weak solutions of higher-order elliptic and parabolic inequalities of the following types: (Formula presented.), where li, mi, ki, ni ∈ N satisfy the condition li, ki > 1 for all i = 1,.., N, and Aαi(x, u), Bβi(x, t, u), f(x, u), and g(x, t, u) are some given Carathéodory functions. Under appropriate conditions on the functions Aαi, Bβi, f, and g, we prove theorems on the nonexistence of solutions of these inequalities. © 2015, Pleiades Publishing, Ltd.