scholarly journals A local existence theorem for a class of delay differential equations

2016 ◽  
pp. 1
Author(s):  
Ioan I. Vrabie
Keyword(s):  
Differential Equations ◽  
Existence Theorem ◽  
Delay Differential Equations ◽  
Local Existence ◽  
Local Existence Theorem ◽  
Delay Differential

scholarly journals An existence theorem for nonlinear delay differential equations

1989 ◽  
Vol 2 (2) ◽  
pp. 85-89
Author(s):  
Krishnan Balachandran
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Existence Theorem ◽  
Delay Differential Equations ◽  
Measure Of Noncompactness ◽  
Existence Of Solutions ◽  
Nonlinear Delay Differential Equations ◽  
Delay Differential ◽  
Nonlinear Delay

In this paper we prove a theorem on the existence of solutions of nonlinear delay differential equations, with implicit derivatives. The result is established using the measure of noncompactness of a set and Darbo's fixed point theorem.

scholarly journals Further results on Ulam stability for a system of first-order nonsingular delay differential equations

2020 ◽  
Vol 53 (1) ◽  
pp. 225-235
Author(s):  
Akbar Zada ◽  
Bakhtawar Pervaiz ◽  
Jehad Alzabut ◽  
Syed Omar Shah
Keyword(s):  
Integral Equation ◽  
Differential Equations ◽  
Existence Theorem ◽  
Delay Differential Equations ◽  
Graphical Representation ◽  
Ulam Stability ◽  
First Order ◽  
Delay Differential ◽  
Unbounded Intervals ◽  
Ulam Type Stability

AbstractThis paper is concerned with a system governed by nonsingular delay differential equations. We study the β-Ulam-type stability of the mentioned system. The investigations are carried out over compact and unbounded intervals. Before proceeding to the main results, we convert the system into an equivalent integral equation and then establish an existence theorem for the addressed system. To justify the application of the reported results, an example along with graphical representation is illustrated at the end of the paper.

scholarly journals On some semilinear equations of Schrödinger type

2002 ◽  
Vol 90 (1) ◽  
pp. 139
Author(s):  
Rossella Agliardi ◽  
Daniela Mari
Keyword(s):  
Differential Equations ◽  
Existence Theorem ◽  
Sobolev Spaces ◽  
Initial Value Problem ◽  
Local Existence ◽  
Weighted Sobolev Spaces ◽  
Initial Value ◽  
Semilinear Equations ◽  
Local Existence Theorem

We study the initial value problem for some semilinear pseudo-differential equations of the form $\partial _tu + i\ H(x,D_x)u = F(u,\nabla u)$. The assumptions we make on $H$ are trivially satisfied by $\Delta$, thus our equations generalize Schrdinger type equations. A local existence theorem is proved in some weighted Sobolev spaces.

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