MULTIPLICITY AND LOCATION RESULTS FOR SECOND ORDER FUNCTIONAL BOUNDARY VALUE PROBLEMS

作者：Fialho J^*; Minhos F

来源：Dynamic Systems and Applications, 2014, 23(2-3): 453-463.

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.

• 出版日期2014-9