Abstract
The authors of this paper prove the existence and regularity results for the homogeneous Dirichlet boundary value problem to the equation- div(M(x)∇un)=f(x)/uα(x)withf∈Lm(Ω) (m⩾ 1)andα(x)>0. The results show the dependence of the summability offin some Lebesgue spaces and on the values ofα(x).
Highlights
The authors of this paper prove the existence and regularity results for the homogeneous Dirichlet boundary value problem to the equation −div(M(x)∇un) = f(x)/uα(x) with f ∈ Lm(Ω) (m ⩾ 1) and α(x) > 0
We study the existence of solutions for the following semilinear elliptic problem with nonlinear singular terms and variable exponent:
U = 0, x ∈ ∂Ω, where Ω is a bounded domain in RN(N ⩾ 2) with smooth boundary ∂Ω, α(x) is a continuous function on Ω, α(x) >
Summary
The results show the dependence of the summability of f in some Lebesgue spaces and on the values of α(x)
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