Abstract
We are concerned with the global structure of positive solutions of the
(
k
,
n
−
k
)
conjugate boundary value problem
(P)
{
(
−
1
)
n
−
k
u
(
n
)
(
t
)
=
λ
a
(
t
)
f
(
u
(
t
)
)
,
0
t
1
,
u
(
i
)
(
0
)
=
0
,
0
≤
i
≤
k
−
1
,
u
(
j
)
(
1
)
=
0
,
0
≤
j
≤
n
−
k
−
1
,
where
n
≥
2
,
1
≤
k
≤
n
,
λ
>
0
is a parameter,
1
≤
k
≤
n
,
λ
>
0
is a parameter,
a
∈
C
(
[
0
,
1
]
,
(
0
,
∞
)
)
and
f
∈
C
(
[
0
,
∞
)
,
[
0
,
∞
)
)
. We obtain existence and multiplicity results for positive solutions of problem
(
P
)
under suitable growth conditions on
f
. The proof of main result is based upon bifurcation techniques.