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

CUBIOTTI, Paolo;
2015-01-01

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.
File in questo prodotto:
File Dimensione Formato  
3061652.pdf

accesso aperto

Tipologia: Versione Editoriale (PDF)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 1.8 MB
Formato Adobe PDF
1.8 MB Adobe PDF Visualizza/Apri
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11570/3061652
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 2
  • ???jsp.display-item.citation.isi??? 2
social impact