Nonlocal eigenvalue problems with indefinite weight
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 کاملOn the Principal Eigenvalue of Some Nonlocal Diffusion Problems
In this paper we analyze some properties of the principal eigenvalue λ1(Ω) of the nonlocal Dirichlet problem (J∗u)(x)−u(x) = −λu(x) in Ω with u(x) = 0 in R \Ω. Here Ω is a smooth bounded domain of R and the kernel J is assumed to be a C compactly supported, even, nonnegative function with unit integral. Among other properties, we show that λ1(Ω) is continuous (or even differentiable) with respe...
متن کاملInverse Eigenvalue Problems for Nonlocal Sturm–liouville Operators
We solve the inverse spectral problem for a class of Sturm–Liouville operators with singular nonlocal potentials and nonlocal boundary conditions.
متن کاملSpectral theory for nonlocal dispersal operators with time periodic indefinite weight functions and applications
In this paper, we study the spectral theory for nonlocal dispersal operators with time periodic indefinite weight functions subject to Dirichlet type, Neumann type and spatial periodic type boundary conditions. We first obtain necessary and sufficient conditions for the existence of a unique positive principal spectrum point for such operators. We then investigate upper bounds of principal spec...
متن کاملPrincipal eigenvalue for an elliptic problem with indefinite weight on cylindrical domains.
This paper is concerned with an indefinite weight linear eigenvalue problem in cylindrical domains. We investigate the minimization of the positive principal eigenvalue under the constraint that the weight is bounded by a positive and a negative constant and the total weight is a fixed negative constant. Biologically, this minimization problem is motivated by the question of determining the opt...
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: Methods of Functional Analysis and Topology
سال: 2020
ISSN: 1029-3531
DOI: 10.31392/mfat-npu26_3.2020.09