Abstract
AbstractHere, we consider the following elliptic problem with variable components: $$ -a(x)\Delta _{p(x)}u - b(x) \Delta _{q(x)}u+ \frac{u \vert u \vert ^{s-2}}{|x|^{s}}= \lambda f(x,u), $$
−
a
(
x
)
Δ
p
(
x
)
u
−
b
(
x
)
Δ
q
(
x
)
u
+
u
|
u
|
s
−
2
|
x
|
s
=
λ
f
(
x
,
u
)
,
with Dirichlet boundary condition in a bounded domain in $\mathbb{R}^{N}$
R
N
with a smooth boundary. By applying the variational method, we prove the existence of at least one nontrivial weak solution to the problem.
Publisher
Springer Science and Business Media LLC
Subject
Algebra and Number Theory,Analysis
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