On the Continuity of Principal Eigenvalues for Boundary Value Problems with Indefinite Weight Function with Respect to Radius of Balls in Rn
نویسنده
چکیده
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 linearized problem
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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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