A discrete three-point boundary value problem Δxk−1 + λ fk(xk)= 0, k = 1,2, . . . ,n, x0 = 0, axl = xn+1, is considered, where 1≤ l ≤ n is a fixed integer, a is a real constant number, and λ is a positive parameter. A characterization of the values of λ is carried out so that the boundary value problem has the positive solutions. Particularly, in this paper the constant a can be negative number...

In this paper, we present the Green’s functions for a second-order linear differential equation with three-point boundary conditions. We give exact expressions of the solutions for the linear three-point boundary problems by the Green’s functions. As applications, we study uniqueness and iteration of the solutions for a nonlinear singular second-order three-point boundary value problem.

In this paper, we investigatethe boundary value problem for differential pencils on the half-linewith a turning point. Using a fundamental system of solutions, wegive a asymptotic distribution of eigenvalues.