Abstract
Abstract
We establish global multiplicity results of solutions for the singular nonlinear problem
0\quad \text{in}\enspace {\Omega},\enspace u=0\enspace \text{on}\enspace \partial {\Omega},\quad \end{cases}\end{equation*}?>
−
Δ
u
−
u
Δ
u
2
=
λ
a
(
x
)
u
−
α
+
b
(
x
)
u
β
in
Ω
,
u
>
0
in
Ω
,
u
=
0
on
∂
Ω
,
where
Ω
⊂
R
N
is a smooth bounded domain; N ⩾ 3; a, b are bounded continuous functions, 0 < α < 1 < β ⩽ 22* − 1 and λ > 0 is a real parameter. We first prove a comparison principle to prove the existence of a minimal solution by the method of sub and super solutions and then we also obtain the second solution by critical point theory.
Funder
National Natural Science Foundation of China
Subject
Applied Mathematics,General Physics and Astronomy,Mathematical Physics,Statistical and Nonlinear Physics
Cited by
8 articles.
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