Study of the Periodic or Nonnegative Periodic Solutions of Functional Differential Equations via Krasnoselskii–Burton’s Theorem
In this paper, we study the existence of periodic or nonnegative periodic solutions of the nonlinear neutral differential equation d d t [ x ( t ) - Q ( t , x ( t - τ ( t ) ) ) ] = - a ( t ) h ( x ( t - τ ( t ) ) ) + G ( t , x ( t ) , x ( t - τ ( t ) ) ) . We invert this equation to construct a sum...
Gespeichert in:
| Veröffentlicht in: | Differential equations and dynamical systems 2016-10, Vol.24 (4), p.391-406 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Zusammenfassung: | In this paper, we study the existence of periodic or nonnegative periodic solutions of the nonlinear neutral differential equation
d
d
t
[
x
(
t
)
-
Q
(
t
,
x
(
t
-
τ
(
t
)
)
)
]
=
-
a
(
t
)
h
(
x
(
t
-
τ
(
t
)
)
)
+
G
(
t
,
x
(
t
)
,
x
(
t
-
τ
(
t
)
)
)
.
We invert this equation to construct a sum of a compact map and a large contraction which is suitable for applying the modification of Krasnoselskii’s theorem. The Caratheodory condition is used for the functions
Q
and
G
. |
|---|---|
| ISSN: | 0971-3514 0974-6870 |
| DOI: | 10.1007/s12591-014-0235-5 |