Positive solution of extremal Pucci’s equations with singular and sublinear nonlinearity

Abstract

In this paper, we establish the existence of a positive solution to {−M+λ,Λ(D2u)=μk(x)f(u)uα−ηh(x)uqu=0in Ωon ∂Ω, {−Mλ,Λ+(D2u)=μk(x)f(u)uα−ηh(x)uqin Ωu=0on ∂Ω, where ΩΩ is a smooth bounded domain in Rn, n≥1.Rn, n≥1. Under certain conditions on k,f and h,k,f and h, using viscosity sub- and super solution method with the aid of comparison principle, we establish the existence of a unique positive viscosity solution. This work extends and complements the earlier works on semilinear and singular elliptic equations with sublinear nonlinearity.