Abstract
In this paper, we consider the following nonlinear eigenvalue problems for the
p
-Laplacian:
−
div
(
a
(
x
)
|
∇
u
|
p
−
2
∇
u
)
=
λ
f
(
x
,
u
)
+
μ
g
(
x
,
u
)
in
R
n
λ
,
μ
>
0
,
lim
|
x
|
→
∞
u
=
0
,
where
1
<
p
<
n
,
λ
,
μ
>
0
,
a
is a measurable bounded function, and
f
and
g
are nonlinearities having subcritical growth with respect to
u
. We prove multiple nontrivial solutions using a recent principle of Ricceri (2009)
[10]. A regularity result is also established.