Abstract
AbstractWe study the one-dimensional nonlocal elliptic equation $$\begin{aligned}& -A\bigl( \bigl\Vert u' \bigr\Vert _{p}^{p} \bigr) u''(x) = \lambda B\bigl( \bigl\Vert u' \bigr\Vert _{q}^{q} \bigr)u(x)^{r} , \quad x \in I:= (0,1), u(x) > 0, x \in I, \\& u(0) = u(1) = 0, \end{aligned}$$
−
A
(
∥
u
′
∥
p
p
)
u
″
(
x
)
=
λ
B
(
∥
u
′
∥
q
q
)
u
(
x
)
r
,
x
∈
I
:
=
(
0
,
1
)
,
u
(
x
)
>
0
,
x
∈
I
,
u
(
0
)
=
u
(
1
)
=
0
,
where $A = A(y)$
A
=
A
(
y
)
and $B = B(y)$
B
=
B
(
y
)
are continuous functions, satisfying $A(y) > 0$
A
(
y
)
>
0
, $B(y) > 0$
B
(
y
)
>
0
for $y > 0$
y
>
0
, $p \ge 1$
p
≥
1
, $q \ge 1$
q
≥
1
, and $r > 1$
r
>
1
are given constants, and $\lambda > 0$
λ
>
0
is a bifurcation parameter. We establish the global behavior of solution curves and precise asymptotic formulas for $u_{\lambda}(x)$
u
λ
(
x
)
as $\lambda \to \infty $
λ
→
∞
.
Funder
Japan Society for the Promotion of Science
Publisher
Springer Science and Business Media LLC
Subject
Algebra and Number Theory,Analysis
Cited by
4 articles.
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