Existence of positive solutions of third-order boundary value problems with integral boundary conditions in Banach spaces
This paper deals with positive solutions of a third-order differential equation in ordered Banach spaces, ( φ ( − x ″ ( t ) ) ) ′ = f ( t , x ( t ) ) , t ∈ J , subject to the following integral boundary conditions: x ( 0 ) = θ , x ″ ( 0 ) = θ , x ( 1 ) = ∫ 0 1 g ( t ) x ( t ) d t , where θ is the ze...
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| Vydáno v: | Advances in difference equations Ročník 2013; číslo 1 |
|---|---|
| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Cham
Springer International Publishing
20.03.2013
|
| Témata: | |
| ISSN: | 1687-1847, 1687-1847 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | This paper deals with positive solutions of a third-order differential equation in ordered Banach spaces,
(
φ
(
−
x
″
(
t
)
)
)
′
=
f
(
t
,
x
(
t
)
)
,
t
∈
J
,
subject to the following integral boundary conditions:
x
(
0
)
=
θ
,
x
″
(
0
)
=
θ
,
x
(
1
)
=
∫
0
1
g
(
t
)
x
(
t
)
d
t
,
where
θ
is the zero element of
E
,
g
∈
L
[
0
,
1
]
is nonnegative,
φ
:
R
→
R
is an increasing and positive homomorphism, and
φ
(
0
)
=
θ
1
. The arguments are based upon the fixed-point principle in cone for strict set contraction operators. Meanwhile, as an application, we also give an example to illustrate our results. |
|---|---|
| ISSN: | 1687-1847 1687-1847 |
| DOI: | 10.1186/1687-1847-2013-65 |