ON A 2-POINT BOUNDARY-VALUE PROBLEM

In this paper we study the two-point boundary value problem y'' = f(t, y, y'), y(0) = y(1) = 0, (P) where f: [0, 1] x R(2) --> R is continuous. By a solution to problem (P) we mean a function y is an element of C-2[0, 1] which satisfies the differential equation and the boundary conditions. We shall impose growth conditions on the function f which enable us to apply the transversality theorem [4] to obtain the existence of a solution to (P). Uniqueness results for (P) are established under a monotonicity requirement on the function f. Our results permit the treatment of equations such as the ones considered in Example 1 and Example 2 below to which the results of [1, 2, 6-16] do not apply.