The purpose of this study is to examine the properties scattering solutions and function an impulsive Sturm-Liouville boundary value problem on semi axis. By using Jost solutions, we obtain function, asymptotic representation resolvent operator. Finally, unperturbated equation.

In previous papers the arithmetic of hierarchical matrices has been described, which allows us to compute the inverse, for instance, of finite element stiffness matrices discretising an elliptic operator L. The required computing time is up to logarithmic factors linear in the dimension of the matrix. In particular, this technique can be used for the computation of the discrete analogue of a re...

In this work, we develop a systematic framework for computing the resolvent of sum two or more monotone operators which only activates each operator in individually. The key tool development is notion “strengthening” set-valued operator, can be viewed as type regularisation that preserves computational tractability. After deriving number iterative schemes through framework, demonstrate their ap...

This work studies the existence and p-th moment asymptotic stability of mild solution some neutral fractional stochastic integro-differential equations involving non-instantaneous impulses Poisson jumps. Sufficient conditions proving solutions are obtained utilizing analysis, resolvent operator Krasnoselskii-Schaefer type fixed point theorem.

An analytical perturbative treatment of characteristic exponents describing the uc-tuations of temporal coarse grained quantities in the context of nonlinear dynamical systems is proposed. It is based on the analysis of the resolvent of the corresponding transfer operator by a projection operator method similar to those used in statistical mechanics. Two diierent approximation schemes are prese...

In this article, we study the asymptotical stability in p-th moment of mild solutions to a class of fractional impulsive partial neutral stochastic integro-differential equations with state-dependent delay in Hilbert spaces. We assume that the linear part of this equation generates an α-resolvent operator and transform it into an integral equation. Sufficient conditions for the existence and as...

This paper is devoted to a class of impulsive fractional semilinear integrodifferential equations with nonlocal initial conditions. Based on the semigroup theory and some fixed point theorems, existence PC-mild solutions established under condition compact resolvent operator. Furthermore, uniqueness proved in case noncompact

In this article we analyze the resolvent, the heat kernel and the spectral zeta function of the operator −d/dr−1/(4r) over the finite interval. The structural properties of these spectral functions depend strongly on the chosen self-adjoint extension of the operator, a choice being made necessary because of the singular potential present. Only for the Friedrichs extension standard properties ar...

We consider Laplacian in a planar strip with Dirichlet boundary condition on the upper boundary and with frequent alternation boundary condition on the lower boundary. The alternation is introduced by the periodic partition of the boundary into small segments on which Dirichlet and Neumann conditions are imposed in turns. We show that under the certain condition the homogenized operator is the ...

This agrees with the definition of the spectrum in the matrix case, where the resolvent set comprises all complex numbers that are not eigenvalues. In terms of its spectrum, we will see that a compact operator behaves like a matrix, in the sense that its spectrum is the union of all of its eigenvalues and 0. We begin with the eigenspaces of a compact operator. We start with two lemmas that we w...