Geodesic
Liouville Theorems for Some Classes of Nonlinear Nonlocal Problems
Informatics and Automation, 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. 
@article{TRSPY_2005_248_a16,
     author = {E. Mitidieri and S. I. Pokhozhaev},
     title = {Liouville {Theorems} for {Some} {Classes} of {Nonlinear} {Nonlocal} {Problems}},
     journal = {Informatics and Automation},
     pages = {164--184},
     publisher = {mathdoc},
     volume = {248},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2005_248_a16/}
}
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E. Mitidieri; S. I. Pokhozhaev. Liouville Theorems for Some Classes of Nonlinear Nonlocal Problems. Informatics and Automation, Studies on function theory and differential equations, Tome 248 (2005), pp. 164-184. http://geodesic.mathdoc.fr/item/TRSPY_2005_248_a16/