Asymptotically linear Schrödinger equation with potential vanishing at infinity
نویسندگان
چکیده
منابع مشابه
Small Time Uniform Controllability of the Linear One-Dimensional Schrödinger Equation with Vanishing Viscosity
This article considers the linear 1-d Schrödinger equation in (0, π) perturbed by a vanishing viscosity term depending on a small parameter ε > 0. We study the boundary controllability properties of this perturbed equation and the behavior of its boundary controls vε as ε goes to zero. It is shown that, for any time T sufficiently large but independent of ε and for each initial datum in H−1(0, ...
متن کاملOn Vanishing at Space Infinity for a Semilinear Heat Equation with Absorption
We consider a Cauchy problem for a semilinear heat equation with absorption. The initial datum of the problem is bounded and its infimum is positive. We study solutions which do not vanish in the total space at the vanishing time; they vanish only at space infinity.
متن کاملSchrödinger equation of general potential
It is well known that the Schrödinger equation is only suitable for the particle in common potential V (~r, t). In this paper, a general Quantum Mechanics is proposed, where the Lagrangian is the general form. The new quantum wave equation can describe the particle which is in general potential V (~r, ~̇r, t). We think these new quantum wave equations can be applied in many fields. PACS numbers:...
متن کاملMorse Complex, Even Functionals and Asymptotically Linear Differential Equations with Resonance at Infinity
I. Motivation. Let H be a Hilbert space and f : H → R a C-functional. To study critical points of f in the framework of the classical approaches (Morse Theory [39], Ljusternik–Schnirelman theory [40], etc.) one needs to assume, in particular, that f satisfies the Palais–Smale condition (in short, PS-condition): any sequence {xn} ⊂ H with {f(xn)} bounded and ∇f(xn) → 0 contains a convergent subs...
متن کاملAsymptotically Flat Initial Data with Prescribed Regularity at Infinity
We prove the existence of a large class of asymptotically flat initial data with non-vanishing mass and angular momentum for which the metric and the extrinsic curvature have asymptotic expansions at space-like infinity in terms of powers of a radial coordinate.
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 Differential Equations
سال: 2008
ISSN: 0022-0396
DOI: 10.1016/j.jde.2008.01.006