scholarly journals Ulam-Hyers stability for partial differential equations

2012 ◽  
Vol 21 (1) ◽  
pp. 73-78
Author(s):  
VASILE L. LAZAR ◽  
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Operator Technique ◽  
Partial Differential ◽  
Picard Operator ◽  
Weakly Picard Operator ◽  
Stability Results

Using the weakly Picard operator technique, we will present some Ulam-Hyers stability results for some partial differential equations.

scholarly journals Existence and Ulam-Hyers stability results for multivalued coincidence problems

Filomat ◽  
2012 ◽  
Vol 26 (5) ◽  
pp. 965-976 ◽  
Author(s):  
Oana Mleşniţe ◽  
Adrian Petruşel
Keyword(s):  
Fixed Point ◽  
Coincidence Point ◽  
Operator Technique ◽  
Picard Operator ◽  
Multivalued Operators ◽  
Weakly Picard Operator ◽  
Stability Results

In this paper, we will present some existence and Ulam-Hyers stability results for fixed point and coincidence point problems with multivalued operators using the weakly Picard operator technique in spaces endowed with vector metrics.

scholarly journals A novel stability analysis for the Darboux problem of partial differential equations via fixed point theory

2021 ◽  
Vol 6 (11) ◽  
pp. 12894-12901
Author(s):  
El-sayed El-hady ◽  
◽  
Abdellatif Ben Makhlouf
Keyword(s):  
Fixed Point ◽  
Stability Analysis ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Fixed Point Theory ◽  
Main Tool ◽  
Point Theory ◽  
Darboux Problem ◽  
Partial Differential ◽  
Stability Results

<abstract><p>We present Ulam-Hyers-Rassias (UHR) stability results for the Darboux problem of partial differential equations (DPPDEs). We employ some fixed point theorem (FPT) as the main tool in the analysis. In this manner, our results are considered as some generalized version of several earlier outcomes.</p></abstract>

scholarly journals Some Properties of Solutions of a Functional-Differential Equation of Second Order with Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Veronica Ana Ilea ◽  
Diana Otrocol
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Operator Theory ◽  
Functional Differential Equations ◽  
Picard Operator ◽  
Functional Differential ◽  
Weakly Picard Operator ◽  
Stability Results

Existence, uniqueness, data dependence (monotony, continuity, and differentiability with respect to parameter), and Ulam-Hyers stability results for the solutions of a system of functional-differential equations with delays are proved. The techniques used are Perov’s fixed point theorem and weakly Picard operator theory.

scholarly journals A Parabolic Transform and Averaging Methods for General Partial Differential Equations

2019 ◽  
Vol 17 ◽  
pp. 352-361
Author(s):  
Mahmoud Mohammed Mostafa El-Borai ◽  
Hamed Kamal Awad Awad ◽  
Randa Hamdy. M. Ali Ali
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Differential Operators ◽  
Averaging Method ◽  
Partial Differential ◽  
Averaging Methods ◽  
Partial Differential Operators ◽  
Existence And Stability ◽  
Special Case ◽  
Stability Results

Averaging method of the fractional general partial differential equations and a special case of these equations are studied, without any restrictions on the characteristic forms of the partial differential operators. We use the parabolic transform, existence and stability results can be obtained.

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