scholarly journals Behavior of the solutions of a partial differential equation with a piecewise constant argument

Filomat ◽  
2017 ◽  
Vol 31 (19) ◽  
pp. 5931-5943 ◽  
Author(s):  
Huseyin Bereketoglu ◽  
Mehtap Lafci
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Existence And Uniqueness ◽  
Partial Differential ◽  
Piecewise Constant ◽  
Piecewise Constant Argument ◽  
Oscillation Instability ◽  
Constant Argument

In this paper, we consider a partial differential equation with a piecewise constant argument. We study existence and uniqueness of the solutions of this equation. We also investigate oscillation, instability and stability of the solutions.

scholarly journals Existence and Uniqueness of Periodic Solutions for a Second-Order Nonlinear Differential Equation with Piecewise Constant Argument

2009 ◽  
Vol 2009 ◽  
pp. 1-14 ◽  
Author(s):  
Gen-qiang Wang ◽  
Sui Sun Cheng
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Periodic Solutions ◽  
Nonlinear Differential Equation ◽  
Existence And Uniqueness ◽  
Second Order ◽  
Piecewise Constant ◽  
Piecewise Constant Argument ◽  
Order Nonlinear Differential Equation ◽  
Constant Argument

Based on a continuation theorem of Mawhin, a unique periodic solution is found for a second-order nonlinear differential equation with piecewise constant argument.

scholarly journals A parabolic differential equation with unbounded piecewise constant delay

1992 ◽  
Vol 15 (2) ◽  
pp. 339-346 ◽  
Author(s):  
Joseph Wiener ◽  
Lokenath Debnath
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Difference Equations ◽  
Infinite Delay ◽  
Parabolic Differential Equation ◽  
Constant Delay ◽  
Partial Differential ◽  
Piecewise Constant ◽  
Greatest Integer Function

A partial differential equation with the argument[λt]is studied, where[•]denotes the greatest integer function. The infinite delayt−[λt]leads to difference equations of unbounded order.

scholarly journals Oscillation criteria for differential equations with piecewise constant argument

2001 ◽  
Vol 32 (4) ◽  
pp. 293-304
Author(s):  
Zhiguo Luo ◽  
Jianhua Shen
Keyword(s):  
Differential Equation ◽  
Continuous Functions ◽  
Variable Coefficients ◽  
Piecewise Constant ◽  
Piecewise Constant Argument ◽  
Greatest Integer Function ◽  
Special Case ◽  
Oscillation And Nonoscillation Criteria ◽  
Oscillation And Nonoscillation ◽  
Constant Argument

We obtain some new oscillation and nonoscillation criteria for the differential equation with piecewise constant argument $$ x'(t) + a(t)x(t) + b(x) x([t-k]) = 0, $$ where $ a(t) $ and $ b(t) $ are continuous functions on $ [-k, \infty) $, $ b(t) \ge 0 $, $ k $ is a positive integer and $ [ \cdot ] $ denotes the greatest integer function. The method used is based on the treatment of certain difference equation with variable coefficients. Our results extend theorems in [15]. As a special case, our results also improve the conclusions obtained by Aftabizadeh, Wiener and Xu [3].

Sign in / Sign up

Export Citation Format

Share Document