English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We consider singular problems of the form −∆u = k (·, u) − h (·, u) in Ω, u = 0 on ∂Ω, u > 0 in Ω, where Ω is a bounded C1,1 domain in Rn, n ≥ 2, h : Ω × [0, ∞) → [0, ∞) and k : Ω × (0, ∞) → [0, ∞) are Carathéodory functions such that h (x, ·) is nondecreasing, and k (x, ·) is nonincreasing and singular at the origin a.e. x ∈ Ω. Additionally, k (·, s) and h (·, s) are allowed to be singular on ∂Ω for s > 0. Under suitable additional hypothesis on h and k, we prove that the stated problem has a unique weak solution u ∈ H1 0 (Ω), and that u belongs to C ( Ω ) . The behavior of the solution near ∂Ω is also addressed.

Positive weak solutions of elliptic Dirichlet problems with singularities in both the dependent and the independent variables