On the Ulam–Hyers stability of first order differential systems with nonlocal initial conditions

2013 ◽  
Vol 82 ◽  
pp. 1-11 ◽  
Author(s):  
Sz. András ◽  
J.J. Kolumbán
Keyword(s):  
Initial Conditions ◽  
Differential Systems ◽  
First Order ◽  
Nonlocal Initial Conditions

scholarly journals Existence of solutions for some nonlinear delay integrodifferential equations with nonlocal initial conditions

2012 ◽  
Vol 45 (1) ◽  
Author(s):  
Zuomao Yan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Existence Of Solutions ◽  
Initial Conditions ◽  
Mild Solutions ◽  
Integrodifferential Equations ◽  
Resolvent Operators ◽  
First Order ◽  
Nonlocal Initial Conditions ◽  
Nonlinear Delay

AbstractThe main purpose of this paper is the existence of mild solutions for a class of first-order nonlinear delay integrodifferential equations with nonlocal initial conditions in Banach spaces. We show that the solutions are given by the application of the theory of resolvent operators and the Sadovskii’s fixed point theorem. An example is presented in the end to show the applications of the obtained results.

scholarly journals EXISTENCE RESULTS FOR IMPULSIVE SYSTEMS WITH INITIAL NONLOCAL CONDITIONS

2013 ◽  
Vol 18 (5) ◽  
pp. 599-611 ◽  
Author(s):  
Octavia Bolojan-Nica ◽  
Gennaro Infante ◽  
Paolamaria Pietramala
Keyword(s):  
Existence Of Solutions ◽  
Initial Conditions ◽  
Nonlocal Conditions ◽  
Impulsive Systems ◽  
First Order ◽  
Nonlocal Initial Conditions ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Fixed Point Principles ◽  
Vector Approach

We study the existence of solutions for nonlinear first order impulsive systems with nonlocal initial conditions. Our approach relies in the fixed point principles of Schauder and Perov, combined with a vector approach that uses matrices that converge to zero. We prove existence and uniqueness results for these systems. Some examples are presented to illustrate the theory.

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