Global asymptotic stability in a class of Putnam-type equations
In this paper, we initiate the study of a class of Putnam-type equation of the form x n + 1 = A 1 x n + A 2 x n - 1 + A 3 x n - 2 x n - 3 + A 4 B 1 x n x n - 1 + B 2 x n - 2 + B 3 x n - 3 + B 4 , n = 0 , 1 , 2 , … , where A 1 , A 2 , A 3 , A 4 , B 1 , B 2 , B 3 , B 4 are positive constants with A 1...
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| Veröffentlicht in: | Nonlinear analysis 2006, Vol.64 (1), p.42-50 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | In this paper, we initiate the study of a class of Putnam-type equation of the form
x
n
+
1
=
A
1
x
n
+
A
2
x
n
-
1
+
A
3
x
n
-
2
x
n
-
3
+
A
4
B
1
x
n
x
n
-
1
+
B
2
x
n
-
2
+
B
3
x
n
-
3
+
B
4
,
n
=
0
,
1
,
2
,
…
,
where
A
1
,
A
2
,
A
3
,
A
4
,
B
1
,
B
2
,
B
3
,
B
4
are positive constants with
A
1
+
A
2
+
A
3
+
A
4
=
B
1
+
B
2
+
B
3
+
B
4
,
x
-
3
,
x
-
2
,
x
-
1
,
x
0
are positive numbers. A sufficient condition is given for the global asymptotic stability of the equilibrium point
c
=
1
of such equations. |
|---|---|
| ISSN: | 0362-546X 1873-5215 |
| DOI: | 10.1016/j.na.2005.06.005 |