Principal Eigenvalues for Problems with Indefinite Weight Function on R
نویسندگان
چکیده
We investigate the existence of positive principal eigenvalues of the problem —Au(x) = lg(x)u for x e R" ; u(x) —* 0 as x —> oo where the weight function g changes sign on R" . It is proved that such eigenvalues exist if g is negative and bounded away from 0 at oo or if n > 3 and \g(x)\ is sufficiently small at oo but do not exist if n = 1 or 2 and fRn g(x)dx > 0 .
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