MULTIPLICITY AND LOCATION RESULTS FOR SECOND ORDER FUNCTIONAL BOUNDARY VALUE PROBLEMS

In this work it is presented some existence, non-existence and location results for the problem composed by the second order fully nonlinear equation (E) u '' (x) + f (x, u (x), u' (x)) = s p(x) for x is an element of [a, b], where f: [a, b] x R-2 -> R, p : [a, b] -> R+ continuous functions and s a real parameter, with the boundary conditions (BC) L-0 (u, u (a), u' (a)) = 0, L-1 (u, u (b), u' (b)) = 0, where L-0 and L-1 are contiunous functions satisfying some adequate monotonicity assumptions. It will be done a discussion on s about the existence and non-existence of solutions for problem (E)-(BC). More precisely, there are s(0), s(1) is an element of R such that: for s < s(0) or (s > s(0)) there is no solution of (E)-(BC). for s = so problem (E)-(BC) has one solution. The arguments used apply lower and upper solutions technique, a Nagumo condition and a priori estimations.