Multiplicity results for a generalized Sturm-Liouville dynamical system on time scales
By applying the fixed point theorem in cones, some new and general results on the existence of positive solution to second order generalized Sturm-Liouville dynamical system on time scale T u 1 Δ Δ ( t ) + h 1 ( t ) f 1 ( t , u 1 ( t ) , u 2 ( t ) , u 1 Δ ( t ) , u 2 Δ ( t ) ) = 0 , u 2 Δ Δ ( t ) +...
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| Published in | Advances in difference equations Vol. 2011; no. 1; pp. 1 - 13 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Cham
Springer International Publishing
15.08.2011
Springer Nature B.V BioMed Central Ltd SpringerOpen |
| Subjects | |
| Online Access | Get full text |
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| Summary: | By applying the fixed point theorem in cones, some new and general results on the existence of positive solution to second order generalized Sturm-Liouville dynamical system on time scale
T
u
1
Δ
Δ
(
t
)
+
h
1
(
t
)
f
1
(
t
,
u
1
(
t
)
,
u
2
(
t
)
,
u
1
Δ
(
t
)
,
u
2
Δ
(
t
)
)
=
0
,
u
2
Δ
Δ
(
t
)
+
h
2
(
t
)
f
2
(
t
,
u
1
(
t
)
,
u
2
(
t
)
,
u
1
Δ
(
t
)
,
u
2
Δ
(
t
)
)
=
0
,
t
∈
[
t
1
,
t
2
]
T
,
a
u
i
(
t
1
)
-
b
u
i
Δ
(
t
1
)
=
∑
k
=
1
m
-
2
a
k
u
i
(
ξ
k
)
,
c
u
i
(
σ
(
t
2
)
)
+
d
u
i
Δ
(
σ
(
t
2
)
)
=
∑
k
=
1
m
-
2
b
k
u
i
(
ξ
k
)
,
(
i
=
1
,
2
)
,
are obtained. The first-order Δ-derivatives are involved in the nonlinear terms explicitly.
Mathematics Subject Classification (2000)
39A10 |
|---|---|
| Bibliography: | SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 ObjectType-Article-2 content type line 23 |
| ISSN: | 1687-1847 1687-1839 1687-1847 |
| DOI: | 10.1186/1687-1847-2011-24 |