Existence of an unbounded branch of the set of solutions for Neumann problems involving the "Equation missing" -Laplacian
We are concerned with the following nonlinear problem: − div ( w ( x ) | ∇ u | p ( x ) − 2 ∇ u ) + | u | p ( x ) − 2 u = μ g ( x ) | u | p ( x ) − 2 u + f ( λ , x , u , ∇ u ) in Ω, ∂ u ∂ n = 0 on ∂ Ω, which is subject to a Neumann boundary condition, provided that μ is not an eigenvalue of the p ( x...
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| Veröffentlicht in: | Boundary value problems 2014-05, Vol.2014 (1), Article 92 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | We are concerned with the following nonlinear problem:
−
div
(
w
(
x
)
|
∇
u
|
p
(
x
)
−
2
∇
u
)
+
|
u
|
p
(
x
)
−
2
u
=
μ
g
(
x
)
|
u
|
p
(
x
)
−
2
u
+
f
(
λ
,
x
,
u
,
∇
u
)
in Ω,
∂
u
∂
n
=
0
on
∂
Ω, which is subject to a Neumann boundary condition, provided that
μ
is not an eigenvalue of the
p
(
x
)
-Laplacian. The aim of this paper is to study the structure of the set of solutions for the degenerate
p
(
x
)
-Laplacian Neumann problems by applying a bifurcation result for nonlinear operator equations.
MSC:
35B32, 35D30, 35J70, 47J10, 47J15. |
|---|---|
| ISSN: | 1687-2770 1687-2770 |
| DOI: | 10.1186/1687-2770-2014-92 |