Liouville Theorems for Some Classes of Nonlinear Nonlocal Problems

This paper is devoted to the further development of the method of nonlinear capacity in the blow-up theory for nonlinear problems. In the framework of this approach, a new class of nonlinear problems with nonlocal nonlinearities is considered, including both stationary and evolution problems. Blow-up criteria depending on the structure of the nonlinear operator and the data of the problem under study are obtained.