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Existence of positive solutions for n + 2 order p -Laplacian BVP
Under some suitable assumptions, we show that the n + 2 order non-linear boundary value problems ( BVP 1 ) { ( E 1 ) [ ϕ p ( u ( n ) ( t ) ) ] ″ = f ( t , u ( t ) , u ( 1 ) ( t ) , … , u ( n + 1 ) ( t ) ) ( BC 1 ) { u ( i ) ( 0 ) = 0 , i = 0 , 1 , 2 , … , n − 3 , u ( n − 1 ) ( 1 ) = 0 u ( n − 2 ) (...
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| Published in: | Computers & mathematics with applications (1987) 2007-05, Vol.53 (9), p.1367-1379 |
|---|---|
| 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: | Under some suitable assumptions, we show that the
n
+
2
order non-linear boundary value problems
(
BVP
1
)
{
(
E
1
)
[
ϕ
p
(
u
(
n
)
(
t
)
)
]
″
=
f
(
t
,
u
(
t
)
,
u
(
1
)
(
t
)
,
…
,
u
(
n
+
1
)
(
t
)
)
(
BC
1
)
{
u
(
i
)
(
0
)
=
0
,
i
=
0
,
1
,
2
,
…
,
n
−
3
,
u
(
n
−
1
)
(
1
)
=
0
u
(
n
−
2
)
(
0
)
=
λ
u
(
n
−
1
)
(
η
)
u
(
n
+
1
)
(
0
)
=
α
1
u
(
n
+
1
)
(
ξ
)
u
(
n
)
(
1
)
=
β
1
u
(
n
)
(
ξ
)
and
(
BVP
2
)
{
(
E
2
)
[
ϕ
p
(
u
(
n
)
(
t
)
)
]
″
=
f
(
t
,
u
(
t
)
,
u
(
1
)
(
t
)
,
…
,
u
(
n
+
1
)
(
t
)
)
(
BC
2
)
{
u
(
i
)
(
0
)
=
0
,
i
=
0
,
1
,
2
,
…
,
n
−
3
,
u
(
n
−
1
)
(
0
)
=
0
u
(
n
−
2
)
(
1
)
=
−
λ
u
(
n
−
1
)
(
η
)
u
(
n
+
1
)
(
0
)
=
α
1
u
(
n
+
1
)
(
ξ
)
u
(
n
)
(
1
)
=
β
1
u
(
n
)
(
ξ
)
have at least two positive solutions in
C
n
[
0
,
1
]
. |
|---|---|
| ISSN: | 0898-1221 1873-7668 |
| DOI: | 10.1016/j.camwa.2006.05.023 |