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Liouville type theorems for integral equations and integral systems. (English) Zbl 1262.45004

The author establishes some Liouville type theorems for positive solutions of integral equations and integral systems in N such as

u(x)= N 1 |x-y| N-α f(u(y))dy,x N ,


u(x)= N 1 |x-y| N-α f(u(y),v(y))dy,x N ,v(x)= R N 1 |x-y| N-α g(u(y),v(y))dy,x N ,

where N2, 0<α<N.

The method of moving planes is used as the main technique.

45G05Singular nonlinear integral equations
45G15Systems of nonlinear integral equations
45M20Positive solutions of integral equations
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