Abstract
AbstractLet 1 < p < N and Ω ⊂ ℝN be an open bounded domain. We study the existence of solutions to equation $$(E) - {\Delta _p}u + g(u)\sigma = \mu $$
(
E
)
−
Δ
p
u
+
g
(
u
)
σ
=
μ
in Ω, where g ∈ C(ℝ) is a nondecreasing function, μ is a bounded Radon measure on Ω and σ is a nonnegative Radon measure on ℝN. We show that if σ belongs to some Morrey space of signed measures, then we may investigate the existence of solutions to equation (E) in the framework of renormalized solutions. Furthermore, imposing a subcritical integral condition on g, we prove that equation (E) admits a renormalized solution for any bounded Radon measure μ. When $$g(t) = |t{|^{q - 1}}t$$
g
(
t
)
=
|
t
|
q
−
1
t
with q > p − 1, we give various sufficient conditions for the existence of renormalized solutions to (E). These sufficient conditions are expressed in terms of Bessel capacities.
Publisher
Springer Science and Business Media LLC
Subject
General Mathematics,Analysis
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