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Multiple positive solutions to some second-order integral boundary value problems with singularity on space variable
This article deals with integral boundary value problems of the second-order differential equations { u ″ ( t ) + a ( t ) u ′ ( t ) + b ( t ) u ( t ) + f ( t , u ( t ) ) = 0 , t ∈ J + , u ( 0 ) = ∫ 0 1 g ( s ) u ( s ) d s , u ( 1 ) = ∫ 0 1 h ( s ) u ( s ) d s , where a ∈ C ( J ) , b ∈ C ( J , R − )...
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| Published in: | Boundary value problems 2017-06, Vol.2017 (1), p.1-10, Article 90 |
|---|---|
| Main Authors: | , |
| 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: | This article deals with integral boundary value problems of the second-order differential equations
{
u
″
(
t
)
+
a
(
t
)
u
′
(
t
)
+
b
(
t
)
u
(
t
)
+
f
(
t
,
u
(
t
)
)
=
0
,
t
∈
J
+
,
u
(
0
)
=
∫
0
1
g
(
s
)
u
(
s
)
d
s
,
u
(
1
)
=
∫
0
1
h
(
s
)
u
(
s
)
d
s
,
where
a
∈
C
(
J
)
,
b
∈
C
(
J
,
R
−
)
,
f
∈
C
(
J
+
×
R
+
,
R
+
)
and
g
,
h
∈
L
1
(
J
)
are nonnegative. The result of the existence of two positive solutions is established by virtue of fixed point index theory on cones. Especially, the nonlinearity
f
permits the singularity on the space variable. |
|---|---|
| ISSN: | 1687-2770 1687-2762 1687-2770 |
| DOI: | 10.1186/s13661-017-0822-9 |