Positivity and lower and upper solutions for fourth order boundary value problems
This paper is devoted to the study the boundary value problem { u ( 4 ) ( t ) = f ( t , u ( t ) ) for all t ∈ I = [ 0 , 1 ] , u ( 0 ) = u ( 1 ) = u ″ ( 0 ) = u ″ ( 1 ) = 0 . We prove the existence of at least one, two or three solutions in the presence of a pair of, not necessarily ordered, lower a...
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| Veröffentlicht in: | Nonlinear analysis 2007-09, Vol.67 (5), p.1599-1612 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | This paper is devoted to the study the boundary value problem
{
u
(
4
)
(
t
)
=
f
(
t
,
u
(
t
)
)
for all
t
∈
I
=
[
0
,
1
]
,
u
(
0
)
=
u
(
1
)
=
u
″
(
0
)
=
u
″
(
1
)
=
0
.
We prove the existence of at least one, two or three solutions in the presence of a pair of, not necessarily ordered, lower and upper solutions.
The proof follows from maximum principles related to the operator
u
(
4
)
+
M
u
and Amann’s three solutions theorem. |
|---|---|
| ISSN: | 0362-546X 1873-5215 |
| DOI: | 10.1016/j.na.2006.08.002 |