Existence and Estimates of Positive Solutions for Some Singular Fractional Boundary Value Problems

摘要

We establish the existence and uniqueness of a positive solutionufor the followingfractional boundary value problem:Dαu(x)=−a(x)uσ(x),x∈(0,1)with the conditionslimx→0+⁡x2−αu(x)=0,u(1)=0, where1<α≤2,σ∈(−1,1), andais a nonnegative continuous function on(0,1)that may be singular atx=0orx=1. We also give the global behavior of such a solution.