scholarly journals Electrostatic-Elastic MEMS with Fringing Field: A Problem of Global Existence

Mathematics ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 54
Author(s):  
Paolo Di Barba ◽  
Luisa Fattorusso ◽  
Mario Versaci
Keyword(s):  
Differential Equation ◽  
Global Existence ◽  
Topological Space ◽  
Existence And Uniqueness ◽  
Industrial Applications ◽  
Nonlocal Model ◽  
Implicit Function ◽  
Uniqueness Of Solutions ◽  
Electrostatic Mems ◽  
Fringing Field

In this paper, we prove the existence and uniqueness of solutions for a nonlocal, fourth-order integro-differential equation that models electrostatic MEMS with parallel metallic plates by exploiting a well-known implicit function theorem on the topological space framework. As the diameter of the domain is fairly small (similar to the length of the device wafer, which is comparable to the distance between the plates), the fringing field phenomenon can arise. Therefore, based on the Pelesko–Driscoll theory, a term for the fringing field has been considered. The nonlocal model obtained admits solutions, making these devices attractive for industrial applications whose intended uses require reduced external voltages.

scholarly journals A necessary and sufficient condition for exponentially bounded existence and uniqueness

1973 ◽  
Vol 8 (1) ◽  
pp. 133-135 ◽  
Author(s):  
David Lowell Lovelady
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Global Existence ◽  
Existence And Uniqueness ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Uniqueness Of Solutions ◽  
Global Existence And Uniqueness ◽  
Necessary And Sufficient

A condition which was previously found to be sufficient for global existence and uniqueness of solutions of an ordinary differential equation is shown herein to be necessary, if it is also required that solutions are exponentially bounded.

scholarly journals About Positivity of Green's Functions for Nonlocal Boundary Value Problems with Impulsive Delay Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Alexander Domoshnitsky ◽  
Irina Volinsky
Keyword(s):  
Differential Equation ◽  
Existence And Uniqueness ◽  
Green's Functions ◽  
Green’S Functions ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Uniqueness Of Solutions ◽  
Impulsive Delay ◽  
Impulsive Delay Differential Equation ◽  
Delay Differential

The impulsive delay differential equation is considered(Lx)(t)=x′(t)+∑i=1mpi(t)x(t-τi(t))=f(t), t∈[a,b],  x(tj)=βjx(tj-0), j=1,…,k, a=t0<t1<t2<⋯<tk<tk+1=b, x(ζ)=0, ζ∉[a,b],with nonlocal boundary conditionlx=∫abφsx′sds+θxa=c,  φ∈L∞a,b;  θ, c∈R.Various results on existence and uniqueness of solutions and on positivity/negativity of the Green's functions for this equation are obtained.

scholarly journals Existence and Uniqueness of Solutions for a Type of Generalized Zakharov System

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Rui Li ◽  
Xing Lin ◽  
Zongwei Ma ◽  
Jingjun Zhang
Keyword(s):  
Cauchy Problem ◽  
Global Existence ◽  
Energy Conservation ◽  
Classical Solution ◽  
Sobolev Spaces ◽  
Existence And Uniqueness ◽  
Uniqueness Of Solutions ◽  
Zakharov System ◽  
The Cauchy Problem ◽  
Global Existence And Uniqueness

We study the Cauchy problem for a type of generalized Zakharov system. With the help of energy conservation and approximate argument, we obtain global existence and uniqueness in Sobolev spaces for this system. Particularly, this result implies the existence of classical solution for this generalized Zakharov system.

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