Eigenvalues of Elliptic Boundary Value Problems With an Indefinite Weight Function
نویسندگان
چکیده
منابع مشابه
Boundedness and Monotonicity of Principal Eigenvalues for Boundary Value Problems with Indefinite Weight Functions
We study the principal eigenvalues (i.e., eigenvalues corresponding to positive eigenfunctions) for the boundary value problem: −∆u(x) = λg(x)u(x), x ∈ D; (∂u/∂n)(x) + αu(x) = 0, x ∈ ∂D, where ∆ is the standard Laplace operator, D is a bounded domain with smooth boundary, g : D → R is a smooth function which changes sign on D and α∈R. We discuss the relation between α and the principal eigenval...
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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: 1986
ISSN: 0002-9947
DOI: 10.2307/2000158