A unified approach to some two-point, three-point, and four-point boundary value problems with Caratheodory functions

[摘要] This paper deals with boundary value problems {-(g(u'))' = f(t, u, u'), a < t < b, u(a) - xi u(alpha) = A, u(b) - eta u(beta) = B and {-(g(u')) = f(t, u, u'), a < t < b, u(a) - xi u(b) = A, u'(b) - eta u'(a) = B, where a < alpha less than or equal to beta < b, xi greater than or equal to 0, eta greater than or equal to 0, A and B are given real numbers, g is a continuous, strictly increasing function with g(R) = R, and f is a Caratheodory function satisfying a Nagumo condition. The problems have solutions if and only if there exist a lower solution x and an upper solution y and x(t) less than or equal to y(t) for all a less than or equal to t less than or equal to b. (C) 1997 Academic Press.

[发布日期] 1997-07-01