Asymptotic solutions for a second-order differential equation with three-point boundary conditions

In this paper, we are concerned with the following singularly perturbed second-order three-point boundary value problem(1.1)y″+(λ2q1(x)+q2(x))y=0,λ≫1,(1.2)y(0)=A,y(1)=αy(η),where 0 < η < 1,A, α ∈ R, λ is a parameter, q1 ∈ C2[0, 1],q2 ∈ C[0, 1]. The asymptotic solutions of the problem are given by using the method of nonlinear analysis and Liouville-Green transform.