Geodesic
Liouville Theorems for Some Classes of Nonlinear Nonlocal Problems
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Studies on function theory and differential equations, Tome 248 (2005), pp. 164-184.

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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. 
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E. Mitidieri; S. I. Pokhozhaev. Liouville Theorems for Some Classes of Nonlinear Nonlocal Problems. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Studies on function theory and differential equations, Tome 248 (2005), pp. 164-184. http://geodesic.mathdoc.fr/item/TM_2005_248_a16/

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