Fractional SchrÖdinger Equations with Singular Potentials of Higher Order. II: Hypoelliptic Case
نویسندگان
چکیده
In this paper we consider the space-fractional Schr\"odinger equation with a singular potential for wide class of fractional hypoelliptic operators. Such analysis can be conveniently realised in setting graded Lie groups. The is continuation and extension previous one where classical on $\mathbb R^n$ potentials was considered.
منابع مشابه
Schrödinger Operators with Singular Potentials †
We describe classical and recent results on the spectral theory of Schrödinger and Pauli operators with singular electric and magnetic potentials
متن کاملSingular Sets of Higher Order Elliptic Equations
The implicit function theorem implies that the zero set of a smooth function, the set where the function vanishes, is a smooth hypersurface away from the critical zero set. Hence to study zero sets it is important to understand the structure of the critical zero sets. For solutions of the second order elliptic equations the critical zero sets represent the singular parts of zero sets. They have...
متن کاملOn Nonexistence of Baras–goldstein Type for Higher-order Parabolic Equations with Singular Potentials
The celebrated result by Baras and Goldstein (1984) established that the heat equation with singular inverse square potential in a smooth bounded domain Ω ⊂ RN , N ≥ 3, such that 0 ∈ Ω, ut = Δu+ c |x|2 u in Ω× (0, T ), u ∣∣ ∂Ω = 0, in the supercritical range c > cHardy(1) = ( N−2 2 )2 , does not have a solution for any nontrivial L1 initial data u0(x) ≥ 0 in Ω or for a positive measure. Namely,...
متن کاملTheory of Hybrid Fractional Differential Equations with Complex Order
We develop the theory of hybrid fractional differential equations with the complex order $thetain mathbb{C}$, $theta=m+ialpha$, $0<mleq 1$, $alphain mathbb{R}$, in Caputo sense. Using Dhage's type fixed point theorem for the product of abstract nonlinear operators in Banach algebra; one of the operators is $mathfrak{D}$- Lipschitzian and the other one is completely continuous, we prove the exis...
متن کاملOn boundary value problems of higher order abstract fractional integro-differential equations
The aim of this paper is to establish the existence of solutions of boundary value problems of nonlinear fractional integro-differential equations involving Caputo fractional derivative by using the techniques such as fractional calculus, H"{o}lder inequality, Krasnoselskii's fixed point theorem and nonlinear alternative of Leray-Schauder type. Examples are exhibited to illustrate the main resu...
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: Reports on Mathematical Physics
سال: 2022
ISSN: ['0034-4877', '1879-0674']
DOI: https://doi.org/10.1016/s0034-4877(22)00010-6