Convergence and asymptotic stability of Galerkin methods for a partial differential equation with piecewise constant argument

2010 ◽  
Vol 217 (2) ◽  
pp. 854-860 ◽  
Author(s):  
Hui Liang ◽  
Dongyang Shi ◽  
Wanjin Lv
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Asymptotic Stability ◽  
Galerkin Methods ◽  
Partial Differential ◽  
Piecewise Constant ◽  
Piecewise Constant Argument ◽  
Constant Argument

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 On a class of third order neutral delay differential equations with piecewise constant argument

1994 ◽  
Vol 17 (1) ◽  
pp. 113-117 ◽  
Author(s):  
Garyfalos Papaschinopoulos
Keyword(s):  
Asymptotic Stability ◽  
Differential Equations ◽  
Delay Differential Equations ◽  
Neutral Delay ◽  
Third Order ◽  
Piecewise Constant ◽  
Piecewise Constant Argument ◽  
Neutral Delay Differential Equations ◽  
Delay Differential ◽  
Constant Argument

In this paper we study existence, uniqueness and asymptotic stability of the solutions of a class of third order neutral delay differential equations 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.

MARKOV SEMIGROUPS AND STABILITY OF THE CELL MATURITY DISTRIBUTION

2000 ◽  
Vol 08 (01) ◽  
pp. 69-94 ◽  
Author(s):  
RYSZARD RUDNICKI ◽  
KATARZYNA PICHÓR
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Asymptotic Stability ◽  
Cell Population ◽  
Markov Semigroups ◽  
Partial Differential ◽  
New Criterion

A model of the maturity-structured cell population is considered. This model is described by a partial differential equation with a transformed argument. Using the theory of Markov semigroups we establish a new criterion for asymptotic stability of such equations.

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 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].

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