Abstract
We study the existence and multiplicity of positive solutions to the periodic problem
u
′′
=
p
(
t
)
u
-
q
(
t
,
u
)
u
+
f
(
t
)
;
u
(
0
)
=
u
(
ω
)
,
u
′
(
0
)
=
u
′
(
ω
)
,
u^{\prime\prime}=p(t)u-q(t,u)u+f(t);\quad u(0)=u(\omega),\quad u^{\prime}(0)=u^{\prime}(\omega),
where
p
,
f
∈
L
(
[
0
,
ω
]
)
p,f\in L([0,\omega])
and
q
:
[
0
,
ω
]
×
R
→
R
q\colon[0,\omega]\times\mathbb{R}\to\mathbb{R}
is a Carathéodory function.
By using the method of lower and upper functions, we show some properties of the solution set of the considered problem and, in particular, the existence of a minimal positive solution.
ON BOUNDARY VALUE PROBLEMS FOR Φ-LAPLACIAN ON THE SEMI-INFINITE INTERVAL
