Affiliation:
1. Mathematics and Computer Science Department , University Abdelmalk Essaadi , National School of Applied Sciences , Al hoceima Morocco .
2. Mathematics and Computer Science Department , University Abdelmalk Essaadi , Sciences and Technologies Faculty , Al hoceima Morocco .
3. Department of Mathematics , University Mohamed I , Multidisciplinary Faculty , Nador Morocco .
Abstract
Abstract
In this paper, we study the following nonlinear eigenvalue problem:
{
Δ
2
p
u
=
λ
m
(
x
)
u
i
n
Ω
,
u
=
Δ
u
=
…
Δ
2
p
−
1
u
=
0
o
n
∂
Ω
.
\left\{ {\matrix{ {{\Delta ^{2p}}u = \lambda m\left( x \right)u\,\,\,in\,\,\Omega ,} \cr {u = \Delta u = \ldots {\Delta ^{2p - 1}}u = 0\,\,\,\,on\,\,\partial \Omega .} \cr } } \right.
Where Ω is a bounded domain in ℝ
N
with smooth boundary ∂ Ω, N ≥ 1, p ∈ ℕ*, m ∈ L∞
(Ω), µ{x ∈ Ω: m(x) > 0} ≠ 0, and Δ2
pu := Δ (Δ...(Δu)), 2p times the operator Δ.
Using the Szulkin’s theorem, we establish the existence of at least one non decreasing sequence of nonnegative eigenvalues.
Subject
Applied Mathematics,Control and Optimization,Numerical Analysis,Analysis
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