Non-real eigenvalues of symmetric Sturm–Liouville problems 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 .
متن کاملBoundedness 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...
متن کاملEigenvalues of the p-Laplacian in RN with indefinite weight
We consider the nonlinear eigenvalue problem − div(|∇u|∇u) = λg(x)|u|u in R with p > 1. A condition on indefinite weight function g is given so that the problem has a sequence of eigenvalues tending to infinity with decaying eigenfunctions in W (R ). A nonexistence result is also given for the case p ≥ N .
متن کاملPrincipal eigenvalues for generalised indefinite Robin problems
We consider the principal eigenvalue of generalised Robin boundary value problems on non-smooth domains, where the zero order coefficient of the boundary operator is negative or changes sign. We provide conditions so that the related eigenvalue problem has a principal eigenvalue. We work with the framework involving measure data on the boundary due to [Arendt & Warma, Potential Anal. 19, 2003, ...
متن کاملInfinite product representation of solution of indefinite SturmLiouville problem
In this paper, we investigate infinite product representation of the solution of a Sturm- Liouville equation with an indefinite weight function which has two zeros and/or singularities in a finite interval. First, by using of the asymptotic estimates provided in [W. Eberhard, G. Freiling, K. Wilcken-Stoeber, Indefinite eigenvalue problems with several singular points and turning points, Math. N...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Electronic Journal of Qualitative Theory of Differential Equations
سال: 2017
ISSN: 1417-3875
DOI: 10.14232/ejqtde.2017.1.18