A class of impulsive nonautonomous differential equations and Ulam-Hyers-Rassias stability

2014 ◽  
Vol 38 (5) ◽  
pp. 868-880 ◽  
Author(s):  
JinRong Wang ◽  
Zeng Lin
Keyword(s):  
Differential Equations ◽  
Nonautonomous Differential Equations ◽  
Rassias Stability

scholarly journals β–Hyers–Ulam–Rassias Stability of Semilinear Nonautonomous Impulsive System

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 231 ◽  
Author(s):  
Xiaoming Wang ◽  
Muhammad Arif ◽  
Akbar Zada
Keyword(s):  
Differential Equations ◽  
Type Inequality ◽  
Impulsive System ◽  
Evolution Family ◽  
Compact Interval ◽  
Ulam Stability ◽  
Basic Tool ◽  
Unbounded Interval ◽  
Nonautonomous Differential Equations ◽  
Rassias Stability

In this paper, we study a system governed by impulsive semilinear nonautonomous differential equations. We present the β –Ulam stability, β –Hyers–Ulam stability and β –Hyers–Ulam–Rassias stability for the said system on a compact interval and then extended it to an unbounded interval. We use Grönwall type inequality and evolution family as a basic tool for our results. We present an example to demonstrate the application of the main result.

scholarly journals The Bohl Spectrum for Linear Nonautonomous Differential Equations

2016 ◽  
Vol 29 (4) ◽  
pp. 1459-1485 ◽  
Author(s):  
Thai Son Doan ◽  
Kenneth J. Palmer ◽  
Martin Rasmussen
Keyword(s):  
Differential Equations ◽  
Nonautonomous Differential Equations

scholarly journals MORSE SPECTRUM FOR NONAUTONOMOUS DIFFERENTIAL EQUATIONS

2008 ◽  
Vol 08 (03) ◽  
pp. 351-363 ◽  
Author(s):  
FRITZ COLONIUS ◽  
PETER E. KLOEDEN ◽  
MARTIN RASMUSSEN
Keyword(s):  
Differential Equations ◽  
Finite Time ◽  
Accumulation Point ◽  
Morse Decomposition ◽  
Finite Time Lyapunov Exponents ◽  
The Past ◽  
Accumulation Points ◽  
Morse Spectrum ◽  
Nonautonomous Differential Equations ◽  
Linear Cocycle

The concept of a Morse decomposition consisting of nonautonomous sets is reviewed for linear cocycle mappings w.r.t. the past, future and all-time convergences. In each case, the set of accumulation points of the finite-time Lyapunov exponents corresponding to points in a nonautonomous set is shown to be an interval. For a finest Morse decomposition, the Morse spectrum is defined as the union of all of the above accumulation point intervals over the different nonautonomous sets in such a finest Morse decomposition. In addition, Morse spectrum is shown to be independent of which finest Morse decomposition is used, when more than one exists.

scholarly journals Stability of Unbounded Differential Equations in Menger k-Normed Spaces: A Fixed Point Technique

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 400 ◽  
Author(s):  
Masoumeh Madadi ◽  
Reza Saadati ◽  
Manuel De la Sen
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Normed Spaces ◽  
Fixed Point Technique ◽  
Rassias Stability

We attempt to solve differential equations υ ′ ( ν ) = Γ ( ν , υ ( ν ) ) and use the fixed point technique to prove its Hyers–Ulam–Rassias stability in Menger k-normed spaces.

Sign in / Sign up

Export Citation Format

Share Document