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Existence of positive solutions of superlinear second-order Neumann boundary value problem
In this paper, we consider the Neumann boundary value problem { − ( p ( t ) u ′ ( t ) ) ′ + q ( t ) u ( t ) = f ( t , u ( t ) ) , t ∈ ( 0 , 1 ) u ′ ( 0 ) = u ′ ( 1 ) = 0 , where p ∈ C 1 [ 0 , 1 ] , p ( t ) > 0 , q ∈ C [ 0 , 1 ] , q ( t ) ≥ 0 , f ∈ C ( [ 0 , 1 ] × ( − ∞ , + ∞ ) , ( − ∞ , + ∞ ) ) ....
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| Published in: | Nonlinear analysis 2010-03, Vol.72 (6), p.3216-3221 |
|---|---|
| Main Author: | |
| Format: | Article |
| Language: | English |
| Subjects: | |
| Citations: | Items that this one cites Items that cite this one |
| Online Access: | Get full text |
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| Summary: | In this paper, we consider the Neumann boundary value problem
{
−
(
p
(
t
)
u
′
(
t
)
)
′
+
q
(
t
)
u
(
t
)
=
f
(
t
,
u
(
t
)
)
,
t
∈
(
0
,
1
)
u
′
(
0
)
=
u
′
(
1
)
=
0
,
where
p
∈
C
1
[
0
,
1
]
,
p
(
t
)
>
0
,
q
∈
C
[
0
,
1
]
,
q
(
t
)
≥
0
,
f
∈
C
(
[
0
,
1
]
×
(
−
∞
,
+
∞
)
,
(
−
∞
,
+
∞
)
)
. By using topological degree theory, we investigate the existence of nontrivial solutions. In particular, we prove the existence of positive solutions provided that
q
(
t
)
>
0
. |
|---|---|
| ISSN: | 0362-546X 1873-5215 |
| DOI: | 10.1016/j.na.2009.12.021 |