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

Abstract EN

We establish the existence and uniqueness of a positive solution u for the following fractional boundary value problem :D α u ( x ) = − a ( x ) u σ ( x ) , x ∈ ( 0 , 1 ) with the conditions lim x → 0 + x 2 − α u ( x ) = 0 , u ( 1 ) = 0 , where 1 < α ≤ 2 , σ ∈ ( − 1 , 1 ) , and a is a nonnegative continuous function on ( 0 , 1 ) that may be singular at x = 0 or x = 1 .

We also give the global behavior of such a solution.