In this paper, we study the parabolic problem associated with non-local conditions, with the Caputo-Fabrizio derivative. Equations on the sphere have many important applications in physics, phenomena, and oceanography. The main motivation for us to study non-local boundary value problems comes from two main reasons: the first reason is that current major interest in several application areas. The second reason is to study approximation for the terminal value problem. With some given data, we prove that the problem has only the solution for two cases. In case = 0, we prove the problem has a local solution. In case > 0, then the problem has a global solution. The main tools and techniques in our demonstration are of using Banach's fixed point theorem in conjunction with some Fourier series analysis involved some evaluation of spherical harmonic function. Several upper and lower upper limit techniques for the Mittag-Lefler functions are also applied.
The present paper addresses questions on resonances for a 1D Schrödinger operator with truncated periodic potential. Precisely, we consider the half-line operatoracting on ℓ 2 (N) with Dirichlet boundary condition at 0 with L ∈ N. We describe the resonances of H N L near the boundary of the essential spectrum of H N as L → +∞ in the generic case, hence complete the results introduced in [10] on the resonances of H N L .
In this article, we prove decorrelation estimates for the eigenvalues of a 1D discrete tight binding model near two distinct energies in the localized regime. Consequently, for any integer n ≥ 2, the asymptotic independence for local level statistics near n distinct energies is obtained.
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