Affiliation:
1. Department of Mathematics, Faculty of Education and Sciences , University of Saba Region , Marib , Yemen
2. Department of Mathematics, Faculty of Sciences , University Abdelmalek Essaadi , , Tetouan , Morocco
Abstract
Abstract
In this paper, we will study the existence of solutions for some nonlinear anisotropic elliptic equation of the type
{
A
u
+
g
(
x
,
u
,
∇
u
)
=
μ
−
d
i
v
φ
(
u
)
i
n
Ω
,
u
=
0
o
n
∂
Ω
,
\left\{ {\matrix{{Au + g\left( {x,u,\nabla u} \right) = \mu - div\,\phi \left( u \right)} \hfill & {in\,\Omega ,} \hfill \cr {u = 0} \hfill & {on\,\,\partial \Omega ,} \hfill \cr } } \right.
where
A
u
=
−
∑
i
=
1
N
∂
∂
x
i
a
i
(
x
,
u
,
∇
u
)
Au = - \sum\limits_{i = 1}^N {{\partial \over {\partial {x_i}}}{a_i}\left( {x,u,\nabla u} \right)}
is a Leray-Lions operator, the Carathéodory function g(x, s, ξ) is a nonlinear lower order term that verify some natural growth and sign conditions, where the data µ = f − div F belongs to L
1−dual and ϕ (·) ∈ C
0(R, R
N
).
Subject
Applied Mathematics,Numerical Analysis,Statistics and Probability,Analysis
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