Eigenvalue inequalities for Schrödinger operators on unbounded Lipschitz domains
نویسندگان
چکیده
منابع مشابه
Nonclassical Eigenvalue Asymptotics for Operators of Schrödinger
which depends on the volume u)n of the unit sphere in R n and the beta function. Assuming /3 < 2 we see that integral (2) becomes divergent if V (x) vanishes to a sufficiently high order. The simplest such potential is V(x,y) = \x\\y\P o n R n + R m . The Weyl (volume counting) principle, when applied to the corresponding Schrödinger operator — A-hV(x), fails to predict discrete spectrum below ...
متن کاملMany Parameter Lipschitz Perturbation of Unbounded Operators
If u 7→ A(u) is a C1,α-mapping having as values unbounded selfadjoint operators with compact resolvents and common domain of definition, parametrized by u in an (even infinite dimensional) space then any continuous arrangement of the eigenvalues u 7→ λi(u) is C0,1 in u. If u 7→ A(u) is C0,1, then the eigenvalues may be chosen C0,1/N (even C0,1 if N = 2), locally in u, where N is locally the max...
متن کاملMultiplicity Results for Nonlinear Eigenvalue Problems on Unbounded Domains
In this paper we prove a multiplicity result for a class of eigenvalue problems with nonlinear boundary conditions on an unbounded domain. Many results have been obtained by Cârstea and Rădulescu [3], Chabrowski [5], [6], Kandilakis and Lyberopoulos [10], Lisei, Varga and Horváth [13] and Pflüger [16]. MSC 2000. 35J60, 35P30, 58E05.
متن کاملEdge currents and eigenvalue estimates for magnetic barrier Schrödinger operators
We study two-dimensional magnetic Schrödinger operators with a magnetic field that is equal to b > 0 for x > 0 and −b for x < 0. This magnetic Schrödinger operator exhibits a magnetic barrier at x = 0. The unperturbed system is invariant with respect to translations in the ydirection. As a result, the Schrödinger operator admits a direct integral decomposition. We analyze the band functions of ...
متن کاملLp Embedding and Nonlinear Eigenvalue Problems for Unbounded Domains
Let R denote real iV-dimensional Euclidean space. Then it is a well-known fact that the imbedding of the Sobolev space Wi,2(R) in LP(R ) is bounded for 2g>pS2N/(N-2), but is definitely not compact. Consequently the theory of critical points for general isoperimetric variational problems defined over arbitrary unbounded domains in R has been little investigated despite its importance. Indeed the...
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: Journal of Spectral Theory
سال: 2018
ISSN: 1664-039X
DOI: 10.4171/jst/203