Asymptotic behavior of positive solutions of a semilinear Dirichlet problem in the annulus

摘要

In this paper, we establish existence and asymptotic behavior of a positive classical solution to the following semilinear boundary value problem: [-Delta u=q(x)u^{sigma };ext{in};Omega,quad u_{|partialOmega}=0.] Here (Omega) is an annulus in (mathbb{R}^{n}), (ngeq 3), (sigma lt 1) and (q) is a positive function in (mathcal{C}_{loc}^{gamma }(Omega )), (0ltgamma lt 1), satisfying some appropriate assumptions related to Karamata regular variation theory. Our arguments combine a method of sub- and supersolutions with Karamata regular variation theory.