scholarly journals Analysis of Volterra integrodifferential equations with nonlocal and boundary conditions via Picard operator

2020 ◽  
Vol 39 (3) ◽  
Author(s):  
Pallavi U. Shikhare ◽  
Kishor D. Kucche ◽  
J. Vanterler da C. Sousa
Keyword(s):  
Boundary Conditions ◽  
Integrodifferential Equations ◽  
Picard Operator

scholarly journals Modeling the Electrostatic Deflection of a MEMS Multilayers Based Actuator

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Hassen M. Ouakad ◽  
Muhammad A. Hawwa ◽  
Hussain M. Al-Qahtani
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Integrodifferential Equations ◽  
Reduced Order Model ◽  
Rigid Substrate ◽  
Order Model ◽  
Commercial Software ◽  
Reduced Order ◽  
Electrostatic Deflection

An actuator comprised of a rigid substrate and two parallel clamped-clamped microbeams is modeled under the influence of electrostatic loading. The problem is considered under the context of nonlinear Euler's mechanics, where the actuating system is described by coupled integrodifferential equations with relevant boundary conditions. Galerkin-based discretization is utilized to obtain a reduced-order model, which is solved numerically. Actuators with different gap sizes between electrode and beams are investigated. The obtained results are compared to simulations gotten by the finite-element commercial software ANSYS.

scholarly journals Existence Theory for Integrodifferential Equations and Henstock-Kurzweil Integral in Banach Spaces

2007 ◽  
Vol 2007 ◽  
pp. 1-12 ◽  
Author(s):  
Aneta Sikorska-Nowak
Keyword(s):  
Banach Space ◽  
Boundary Conditions ◽  
Banach Spaces ◽  
Integrodifferential Equation ◽  
Measure Of Noncompactness ◽  
Existence Theorems ◽  
Integrodifferential Equations ◽  
Existence Theory

We prove existence theorems for the integrodifferential equationx'(t)=f(t,x(t),∫0tk(t,s,x(s))ds),x(0)=x0,t∈Ia=[0,a],a>0, wheref,k,xare functions with values in a Banach spaceEand the integral is taken in the sense of HL. Additionally, the functionsfandksatisfy certain boundary conditions expressed in terms of the measure of noncompactness.

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