Two-Point Problems for Non-Linear Second Order Ordinary Differential Equations

摘要

This paper considers the differential equation y'' + F (t,y,y') = 0 together with one of the boundary conditions y(a) = A and y(b) = B, y(a) = A and y'(b) = B, y'(a) = A and y(b) = B. Under appropriate conditions on F, it is well-known that, for fixed a, a unique solution exists if b - a is small enough. The question of a bound for b - a continues to be of interest. Techniques are developed which provide some insight into previous proofs and give improvements of known results. In some cases the results can be interpreted as disconjugacy or non-oscillation theorems. (Author)