Existence of solutions for a nonhomogeneous semilinear elliptic equation. (June 2020) - Arcoya, David; de Paiva, Francisco Odair; Mendoza, José M.
Abstract: For a bounded domain Ω, a bounded Carathéodory function g in Ω × R, p > 1 and a nonnegative locally integrable function h in Ω which is strictly positive in a set of positive measure we prove that, contrarily with the case h ≡ 0, there exists a solution of the semilinear elliptic problem − Δ u = λ u + g ( x, u ) − h | u | p − 1 u + f, in Ω u = 0, on ∂ Ω, for every λ ∈ R and f ∈ L 2 ( Ω ) .