Principal Eigenvalues with Indefinite Weight Functions
نویسندگان
چکیده
منابع مشابه
Principal Eigenvalues for Problems with Indefinite Weight Function on R
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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where D is a bounded domain with smooth boundary, g changes sign on D, and f is some function of class C1 such that f(0)= 0= f(1). Fleming’s results suggested that nontrivial steady-state solutions were bifurcating the trivial solutions u ≡ 0 and u ≡ 1. In order to investigate these bifurcation phenomena, it was necessary to understand the eigenvalues and eigenfunctions of the corresponding lin...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1997
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-97-01797-2