Affiliation:
1. School of Mathematical Sciences, Shanxi University, Taiyuan 030006, Shanxi, China
Abstract
Abstract
In this paper,
Morse theory is used to study the existence and multiplicity of nontrivial solutions for the following class of quasilinear elliptic equations:
{
-
Δ
u
-
Δ
(
u
2
)
u
=
g
(
x
,
u
)
,
x
∈
Ω
,
u
=
0
,
x
∈
∂
Ω
,
$\left\{\begin{aligned} &\displaystyle{-}\Delta u-\Delta(u^{2})u=g(x,u),&&%
\displaystyle x\in\Omega,\\
&\displaystyle u=0,&&\displaystyle x\in\partial\Omega,\end{aligned}\right.$
where
Ω
⊂
ℝ
N
${\Omega\subset\mathbb{R}^{N}}$
is a bounded open domain with smooth boundary
∂
Ω
${\partial\Omega}$
,
N
⩾
3
${N\geqslant 3}$
and g is a Carathéodory function with some additional growth conditions.
Funder
National Natural Science Foundation of China
Subject
General Mathematics,Statistical and Nonlinear Physics
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