scholarly journals On the concept and existence of solutions for fractional impulsive systems with Hadamard derivatives

2015 ◽  
Vol 39 ◽  
pp. 85-90 ◽  
Author(s):  
JinRong Wang ◽  
Yuruo Zhang
Keyword(s):  
Existence Of Solutions ◽  
Impulsive Systems

scholarly journals Existence Conditions for Bounded Solutions of Weakly Perturbed Linear Impulsive Systems

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
Alexander Boichuk ◽  
Martina Langerová ◽  
Jaroslava Škoríková
Keyword(s):  
Small Parameter ◽  
Real Axis ◽  
Laurent Series ◽  
Existence Of Solutions ◽  
Bounded Solutions ◽  
Impulsive Systems ◽  
Entire Real Axis ◽  
Existence Conditions ◽  
Generating System

The weakly perturbed linear nonhomogeneous impulsive systems in the formẋ=A(t)x  +  εA1(t)x  +  f(t),  t∈R,  t∉T:={τi}Z,Δx|t=τi=γi+εA1ix(τi-),  τi∈T⊂R,  γi∈Rn, andi∈Zare considered. Under the assumption that the generating system (forε=0) does not have solutions bounded on the entire real axis for some nonhomogeneities and using the Vishik-Lyusternik method, we establish conditions for the existence of solutions of these systems bounded on the entire real axis in the form of a Laurent series in powers of small parameterεwith finitely many terms with negative powers ofε, and we suggest an algorithm of construction of these solutions.

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.

scholarly journals Stability of Ulam–Hyers and Existence of Solutions for Impulsive Time-Delay Semi-Linear Systems with Non-Permutable Matrices

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1493
Author(s):  
Nazim I. Mahmudov ◽  
Amal M. Almatarneh
Keyword(s):  
Time Delay ◽  
Existence Of Solutions ◽  
Linear Time ◽  
Sufficient Conditions ◽  
Representation Formula ◽  
Matrix Exponential ◽  
Delay Systems ◽  
Impulsive Systems ◽  
Impulsive Delay ◽  
The Stability

In this paper, the stability of Ulam–Hyers and existence of solutions for semi-linear time-delay systems with linear impulsive conditions are studied. The linear parts of the impulsive systems are defined by non-permutable matrices. To obtain solution for linear impulsive delay systems with non-permutable matrices in explicit form, a new concept of impulsive delayed matrix exponential is introduced. Using the representation formula and norm estimation of the impulsive delayed matrix exponential, sufficient conditions for stability of Ulam–Hyers and existence of solutions are obtained.

Optimal control of switched impulsive systems with time delay

2013 ◽  
Vol 53 ◽  
pp. 291
Author(s):  
Wan Mei Tang ◽  
Kar Hung Wong
Keyword(s):  
Optimal Control ◽  
Time Delay ◽  
Impulsive Systems

Existence of solutions for a second order boundary value problem with the Clarke subdifferential

Filomat ◽  
2017 ◽  
Vol 31 (9) ◽  
pp. 2763-2771 ◽  
Author(s):  
Dalila Azzam-Laouir ◽  
Samira Melit
Keyword(s):  
Boundary Value Problem ◽  
Differential Inclusion ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Second Order ◽  
Clarke Subdifferential ◽  
Lipschitzian Function ◽  
The Clarke Subdifferential

In this paper, we prove a theorem on the existence of solutions for a second order differential inclusion governed by the Clarke subdifferential of a Lipschitzian function and by a mixed semicontinuous perturbation.

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