scholarly journals Positive periodic solutions in shifts δ ± for a nonlinear first-order functional dynamic equation on time scales

2014 ◽  
Vol 2014 (1) ◽  
Author(s):  
Erbil Çetin
Keyword(s):  
Periodic Solutions ◽  
Time Scales ◽  
Dynamic Equation ◽  
Positive Periodic Solutions ◽  
First Order

scholarly journals Existence of positive periodic solutions in shifts δ± for a nonlinear first order functional dynamic equation on time scales

Filomat ◽  
2016 ◽  
Vol 30 (9) ◽  
pp. 2551-2571
Author(s):  
Erbil Çetin ◽  
Serap Topal
Keyword(s):  
Fixed Point ◽  
Periodic Solutions ◽  
Time Scales ◽  
Dynamic Equation ◽  
Fixed Point Theorems ◽  
Sufficient Conditions ◽  
Positive Periodic Solutions ◽  
Nonlinear Functional ◽  
First Order ◽  
Nonexistence And Existence

Let T ? R be a periodic time scale in shifts ?? with period P ? [t0,?)T. In this paper we consider the nonlinear functional dynamic equation of the form x?(t) = a(t)x(t)- ?b(t) f (x(h(t))), t ? T. By using the Krasnoselski?, Avery-Henderson and Leggett-Williams fixed point theorems, we present different sufficient conditions for the nonexistence and existence of at least one, two or three positive periodic solutions in shifts ?? of the above problem on time scales. We extend and unify periodic differential, difference, h-difference and q-difference equations and more by a new periodicity concept on time scales.

scholarly journals EXISTENCE AND EXPONENTIAL STABILITY OF POSITIVE PERIODIC SOLUTIONS FOR SECOND-ORDER DYNAMIC EQUATIONS

2020 ◽  
Vol 6 (1) ◽  
pp. 42
Author(s):  
Faycal Bouchelaghem ◽  
Abdelouaheb Ardjouni ◽  
Ahcene Djoudi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Exponential Stability ◽  
Periodic Solutions ◽  
Time Scales ◽  
Point Theorem ◽  
Second Order ◽  
Dynamic Equations ◽  
Positive Periodic Solutions ◽  
Main Method

In this article, we establish the existence of positive periodic solutions for second-order dynamic equations on time scales. The main method used here is the Schauder fixed point theorem. The exponential stability of positive periodic solutions is also studied. The results obtained here extend some results in the literature. An example is also given to illustrate this work.

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