scholarly journals On the representation of solutions of some classes of two-linear dimensional difference equations

2021 ◽  
Vol 57 (2) ◽  
pp. 190-197
Author(s):  
R. R. Amirova ◽  
Zh. B. Ahmedova ◽  
K. B. Mansimov
Keyword(s):  
Difference Equations ◽  
Two Dimensional ◽  
Volterra Type ◽  
Riemann Matrix ◽  
Representation Of Solutions

Herein, some classes of linear two-dimensional difference equations of Volterra type are considered. Representations of solutions using analogs of the resolvent and the Riemann matrix are obtained.

Lateral structure-foundation interaction of structures with base masses

1972 ◽  
Vol 62 (2) ◽  
pp. 453-470
Author(s):  
R. J. Scavuzzo ◽  
D. D. Raftopoulos ◽  
J. L. Bailey
Keyword(s):  
Integral Equation ◽  
Free Field ◽  
Response Spectra ◽  
Elastic Half Space ◽  
Two Dimensional ◽  
Transient Solution ◽  
Volterra Type ◽  
Seismic Motion ◽  
Lateral Structure ◽  
Inertia Forces

abstract The interaction of lateral inertia forces of an N-mass structure with a base mass and lateral seismic motion of the foundation is formulated as an integral equation of the Volterra type. Flexibility of the foundation is based on the transient solution of a two-dimensional elastic half-space. Interaction effects are evaluated by comparing the response spectra of the free-field motion to that of the foundation motion. Results show that changes in the response spectra are significant for heavy, stiff structures such as a reactor-containment vessel.

scholarly journals Asymptotic Properties of Solutions to Second-Order Difference Equations of Volterra Type

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Janusz Migda ◽  
Małgorzata Migda ◽  
Magdalena Nockowska-Rosiak
Keyword(s):  
Asymptotic Behavior ◽  
Difference Equations ◽  
Existence Of Solutions ◽  
Asymptotic Properties ◽  
Sufficient Conditions ◽  
Type Equation ◽  
Asymptotic Behavior Of Solutions ◽  
Volterra Type ◽  
Order Difference ◽  
Prescribed Asymptotic Behavior

We consider the discrete Volterra type equation of the form Δ(rnΔxn)=bn+∑k=1nK(n,k)f(xk). We present sufficient conditions for the existence of solutions with prescribed asymptotic behavior. Moreover, we study the asymptotic behavior of solutions. We use o(ns), for given nonpositive real s, as a measure of approximation.

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