Constant-sign and sign-changing solutions for the Sturm–Liouville boundary value problems
In this paper, we study the Strum–Liouville boundary value problem - ( p ( x ) u ′ ( x ) ) ′ + q ( x ) u ( x ) = f ( x , u ( x ) ) , 0 ≤ x ≤ 1 , α u ′ ( 0 ) - β u ( 0 ) = 0 , γ u ′ ( 1 ) + σ u ( 1 ) = 0 . Using critical point theory and suitable truncation techniques, we prove the existence of two o...
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| Veröffentlicht in: | Monatshefte für Mathematik 2016-01, Vol.179 (1), p.41-55 |
|---|---|
| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | In this paper, we study the Strum–Liouville boundary value problem
-
(
p
(
x
)
u
′
(
x
)
)
′
+
q
(
x
)
u
(
x
)
=
f
(
x
,
u
(
x
)
)
,
0
≤
x
≤
1
,
α
u
′
(
0
)
-
β
u
(
0
)
=
0
,
γ
u
′
(
1
)
+
σ
u
(
1
)
=
0
.
Using critical point theory and suitable truncation techniques, we prove the existence of two opposite constant sign solutions and infinitely many sign-changing solutions of the problem. Different from the existing research, we do not impose any restrictions to the behavior of the nonlinear term
f
at infinity. |
|---|---|
| ISSN: | 0026-9255 1436-5081 |
| DOI: | 10.1007/s00605-014-0694-3 |