Asymptotic behavior of positive solutions of a semilinear Dirichlet problem Original Research Article

In this paper, we study the asymptotic behavior of the unique positive classical solution to the following semilinear boundary value problem View the MathML sourceΔu+a(x)uα=0, x∈Ω, u>0 in Ω, u|∂Ω=0. Turn MathJax on Here View the MathML sourceΩ is a bounded C1,1C1,1 domain, α<1α<1 and the function aa is in View the MathML sourceClocγ(Ω), 0<γ<10<γ<1 such that there exists c>0c>0 satisfying for each View the MathML sourcex∈Ω, View the MathML source1c≤a(x)δ(x)λexp(−∫δ(x)ηz(t)tdt)≤c, Turn MathJax on where λ≤2λ≤2, View the MathML sourceη>d=diam(Ω), δ(x)δ(x)View the MathML source=dist(x,∂Ω) and zz is a continuous function on [0,η][0,η] with z(0)=0z(0)=0.