scholarly journals Oscillatory and periodic solutions in alternately advanced and delayed differential equations

2013 ◽  
Vol 29 (2) ◽  
pp. 149-158
Author(s):  
KUO-SHOU CHIU ◽  
◽  
MANUEL PINTO ◽  
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Piecewise Constant ◽  
Piecewise Constant Argument ◽  
Delayed Differential Equations ◽  
Existence Of Periodic Solutions ◽  
Constant Argument

We examine scalar differential equations with a general piecewise constant argument (DEPCAG). It is shown that the argument deviation generates, under certain conditions, oscillations of the solutions, which is an impossible phenomenon for the corresponding equation without the argument deviations. Criteria for existence of periodic solutions of such equations are discussed.

scholarly journals THREE POSITIVE PERIODIC SOLUTIONS FOR DYNAMIC EQUATIONS WITH PIECEWISE CONSTANT ARGUMENT AND IMPULSE ON TIME SCALES

2010 ◽  
Vol 53 (2) ◽  
pp. 369-377 ◽  
Author(s):  
YONGKUN LI ◽  
ERLIANG XU
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Time Scales ◽  
Dynamic Equations ◽  
Positive Periodic Solutions ◽  
Piecewise Constant ◽  
Piecewise Constant Argument ◽  
Constant Argument

AbstractIn this paper, by using the Leggett–Williams fixed point theorem, the existence of three positive periodic solutions for differential equations with piecewise constant argument and impulse on time scales is investigated. Some easily verifiable sufficient criteria are established. Finally, an example is given to illustrate the results.

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