Open AccessExistence of positive periodic solutions in shifts δ± for a nonlinear first order functional dynamic equation on time scales
Author(s) -
Erbil Çetin,
Fatma Serap Topal
Publication year - 2016
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil1609551c
Subject(s) - mathematics , nonlinear system , dynamic equation , order (exchange) , differential equation , scale (ratio) , period (music) , mathematical analysis , fixed point theorem , pure mathematics , physics , quantum mechanics , finance , economics , acoustics
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.