Liouville-Type Theorems for Some Integral Systems
نویسنده
چکیده
/2 ( ) ( ) u u where is the Fourier transformation and its inverse. The question is to determine for which values of the exponents pi and qi the only nonnegative solution (u, v) of (1) and (2) is trivial, i.e., (u; v) = (0, 0). When 2 , is the case of the Emden-Fowler equation 0 , 0 u u u k in N (5) When ) 3 )( 2 /( ) 2 ( 1 N N N k , it has been proved in [3,4] that the only solutions of (5) is u = 0. In dimension N = 2, a similar conclusion holds for k 0 . It is also well known that in the critical case, / ) 2 ( N k ) 2 ( N , problem (5) has a two-parameter family of solutions given by
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