Given a multifunction F : [a, b] x R-n x R-n -> 2(R) and a function h : X -> R (with X subset of R-n), we consider the following implicit two-point problem: find u is an element of W-2,W-p([a,b], R-n) such that {h(u ''(t)) is an element of F(t, u(t), u'(t)) a.e. in [a, b], u(a) = u(b) = 0(Rn). We prove an existence theorem where, for each t is an element of [a, b], the multifunction F(t, .,.) can fail to be lower semicontinuous even at all points (x, y) is an element of R-n xR(n). The function h is assumed to be continuous and locally nonconstant.

### A boundary value problem for implicit vector differential inclusions without assumptions of lower semicontinuity

#### Abstract

Given a multifunction F : [a, b] x R-n x R-n -> 2(R) and a function h : X -> R (with X subset of R-n), we consider the following implicit two-point problem: find u is an element of W-2,W-p([a,b], R-n) such that {h(u ''(t)) is an element of F(t, u(t), u'(t)) a.e. in [a, b], u(a) = u(b) = 0(Rn). We prove an existence theorem where, for each t is an element of [a, b], the multifunction F(t, .,.) can fail to be lower semicontinuous even at all points (x, y) is an element of R-n xR(n). The function h is assumed to be continuous and locally nonconstant.
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11570/3061652`
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