Continuous Dependence and Differentiability of Solutions of Second-Order Impulsive Differential Equations on Initial Values and Impulsive Points

2021 ◽  
Vol 20 (3) ◽  
Author(s):  
Qian Wen ◽  
JinRong Wang
Keyword(s):  
Differential Equations ◽  
Continuous Dependence ◽  
Impulsive Differential Equations ◽  
Second Order ◽  
Initial Values ◽  
Differentiability Of Solutions

scholarly journals Second-order impulsive differential systems with mixed and several delays

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Shyam Sundar Santra ◽  
Apurba Ghosh ◽  
Omar Bazighifan ◽  
Khaled Mohamed Khedher ◽  
Taher A. Nofal
Keyword(s):  
Differential Equations ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Oscillation Theory ◽  
Second Order ◽  
Neutral Delay ◽  
Differential Systems ◽  
Impulsive Differential Systems ◽  
Several Delays ◽  
Necessary And Sufficient

AbstractIn this work, we present new necessary and sufficient conditions for the oscillation of a class of second-order neutral delay impulsive differential equations. Our oscillation results complement, simplify and improve recent results on oscillation theory of this type of nonlinear neutral impulsive differential equations that appear in the literature. An example is provided to illustrate the value of the main results.

scholarly journals New Results on Qualitative Behavior of Second Order Nonlinear Neutral Impulsive Differential Systems with Canonical and Non-Canonical Conditions

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 934
Author(s):  
Shyam Sundar Santra ◽  
Khaled Mohamed Khedher ◽  
Kamsing Nonlaopon ◽  
Hijaz Ahmad
Keyword(s):  
Asymptotic Behavior ◽  
Differential Equations ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Oscillatory Behavior ◽  
Second Order ◽  
Discrete Equation ◽  
Qualitative Behavior ◽  
Differential Systems ◽  
Impulsive Differential Systems

The oscillation of impulsive differential equations plays an important role in many applications in physics, biology and engineering. The symmetry helps to deciding the right way to study oscillatory behavior of solutions of impulsive differential equations. In this work, several sufficient conditions are established for oscillatory or asymptotic behavior of second-order neutral impulsive differential systems for various ranges of the bounded neutral coefficient under the canonical and non-canonical conditions. Here, one can see that if the differential equations is oscillatory (or converges to zero asymptotically), then the discrete equation of similar type do not disturb the oscillatory or asymptotic behavior of the impulsive system, when impulse satisfies the discrete equation. Further, some illustrative examples showing applicability of the new results are included.

scholarly journals Bounded Oscillation Theorem for Unstable-type Neutral Impulsive Differential Equations of the Second Order

2019 ◽  
pp. 1-9
Author(s):  
U. A. Abasiekwere ◽  
E. Eteng ◽  
I. O. Isaac ◽  
Z. Lipcsey
Keyword(s):  
Differential Equations ◽  
Transmission Lines ◽  
High Speed ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Central Place ◽  
Oscillatory Solution ◽  
Second Order ◽  
Oscillation Theorem ◽  
Neutral Differential Equations

The oscillations theory of neutral impulsive differential equations is gradually occupying a central place among the theories of oscillations of impulsive differential equations. This could be due to the fact that neutral impulsive differential equations plays fundamental and significant roles in the present drive to further develop information technology. Indeed, neutral differential equations appear in networks containing lossless transmission lines (as in high-speed computers where the lossless transmission lines are used to interconnect switching circuits).   In this paper, we study the behaviour of solutions of a certain class of second-order linear neutral differential equations with impulsive constant jumps.  This type of equation in practice is always known to have an unbounded non-oscillatory solution.  We, therefore, seek sufficient conditions for which all bounded solutions are oscillatory and provide an example to demonstrate the applicability of the abstract result.

scholarly journals Infinite Boundary Value Problems for Second-Order Nonlinear Impulsive Differential Equations with Supremum

2010 ◽  
Vol 2010 ◽  
pp. 1-15
Author(s):  
Piao-Piao Shi ◽  
Wen-Xia Wang
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Solution Method ◽  
Boundary Value ◽  
Impulsive Differential Equations ◽  
Existence Results ◽  
Second Order ◽  
Comparison Result ◽  
Upper Solution ◽  
Lower And Upper Solution

We investigate the infinite boundary value problems for second-order impulsive differential equations with supremum by establishing a new comparison result and using the lower and upper solution method, and obtain the existence results for their maximal and minimal solutions.

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