Numerical extremal solutions for a mixed problem with singular ϕ -Laplacian
We are concerned with extremal solutions for the mixed boundary value problem - r N - 1 ϕ ( u ′ ) ′ = r N - 1 g ( r , u ) , u ′ ( 0 ) = 0 = u ( R ) , where g : [ 0 , R ] × R → R is a continuous function and ϕ : ( - η , η ) → R is an increasing homeomorphism with ϕ ( 0 ) = 0 . We prove the existence...
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| Veröffentlicht in: | Nonlinear differential equations and applications 2014-04, Vol.21 (2), p.289-304 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | We are concerned with extremal solutions for the mixed boundary value problem
-
r
N
-
1
ϕ
(
u
′
)
′
=
r
N
-
1
g
(
r
,
u
)
,
u
′
(
0
)
=
0
=
u
(
R
)
,
where
g
:
[
0
,
R
]
×
R
→
R
is a continuous function and
ϕ
:
(
-
η
,
η
)
→
R
is an increasing homeomorphism with
ϕ
(
0
)
=
0
.
We prove the existence of minimal and maximal solutions in presence of well-ordered lower and upper solutions and develop a numerical algorithm for theirs approximation. Also, we provide numerical experiments confirming the theoretical aspects. |
|---|---|
| ISSN: | 1021-9722 1420-9004 |
| DOI: | 10.1007/s00030-013-0247-9 |