Bounded Palais-Smale sequences for non-differentiable functions

Roberto Livrea, Roberto Livrea, Pasquale Candito, Dumitru Motreanu

Risultato della ricerca: Article

2 Citazioni (Scopus)

Abstract

The existence of bounded Palais-Smale sequences (briefly BPS) for functionals depending on a parameter belonging to a real interval and which are the sum of a locally Lipschitz continuous term and of a convex, proper, lower semicontinuous function, is obtained when the parameter runs in a full measure subset of the given interval. Specifically, for this class of non-smooth functions, we obtain BPS related to mountain pass and to global infima levels. This is done by developing a unifying approach, which applies to both cases and relies on a suitable deformation lemma. © 2011 Elsevier Ltd. All rights reserved.
Lingua originaleEnglish
pagine (da-a)5446-5454
Numero di pagine9
RivistaNONLINEAR ANALYSIS
Volume74
Stato di pubblicazionePublished - 2011

Fingerprint

Mountain Pass
Lower Semicontinuous Function
Nonsmooth Function
Interval
Lipschitz
Lemma
Subset
Term
Class

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Cita questo

Livrea, R., Livrea, R., Candito, P., & Motreanu, D. (2011). Bounded Palais-Smale sequences for non-differentiable functions. NONLINEAR ANALYSIS, 74, 5446-5454.

Bounded Palais-Smale sequences for non-differentiable functions. / Livrea, Roberto; Livrea, Roberto; Candito, Pasquale; Motreanu, Dumitru.

In: NONLINEAR ANALYSIS, Vol. 74, 2011, pag. 5446-5454.

Risultato della ricerca: Article

Livrea, R, Livrea, R, Candito, P & Motreanu, D 2011, 'Bounded Palais-Smale sequences for non-differentiable functions', NONLINEAR ANALYSIS, vol. 74, pagg. 5446-5454.
Livrea, Roberto ; Livrea, Roberto ; Candito, Pasquale ; Motreanu, Dumitru. / Bounded Palais-Smale sequences for non-differentiable functions. In: NONLINEAR ANALYSIS. 2011 ; Vol. 74. pagg. 5446-5454.
@article{18a115d9ff684c73a8cf77d9ecfe41dd,
title = "Bounded Palais-Smale sequences for non-differentiable functions",
abstract = "The existence of bounded Palais-Smale sequences (briefly BPS) for functionals depending on a parameter belonging to a real interval and which are the sum of a locally Lipschitz continuous term and of a convex, proper, lower semicontinuous function, is obtained when the parameter runs in a full measure subset of the given interval. Specifically, for this class of non-smooth functions, we obtain BPS related to mountain pass and to global infima levels. This is done by developing a unifying approach, which applies to both cases and relies on a suitable deformation lemma. {\circledC} 2011 Elsevier Ltd. All rights reserved.",
keywords = "Bounded Palais-Smale sequences, Critical points, Deformation, Mountain pass geometry, Non-smooth functions",
author = "Roberto Livrea and Roberto Livrea and Pasquale Candito and Dumitru Motreanu",
year = "2011",
language = "English",
volume = "74",
pages = "5446--5454",
journal = "Nonlinear Analysis, Theory, Methods and Applications",
issn = "0362-546X",
publisher = "Elsevier Ltd",

}

TY - JOUR

T1 - Bounded Palais-Smale sequences for non-differentiable functions

AU - Livrea, Roberto

AU - Livrea, Roberto

AU - Candito, Pasquale

AU - Motreanu, Dumitru

PY - 2011

Y1 - 2011

N2 - The existence of bounded Palais-Smale sequences (briefly BPS) for functionals depending on a parameter belonging to a real interval and which are the sum of a locally Lipschitz continuous term and of a convex, proper, lower semicontinuous function, is obtained when the parameter runs in a full measure subset of the given interval. Specifically, for this class of non-smooth functions, we obtain BPS related to mountain pass and to global infima levels. This is done by developing a unifying approach, which applies to both cases and relies on a suitable deformation lemma. © 2011 Elsevier Ltd. All rights reserved.

AB - The existence of bounded Palais-Smale sequences (briefly BPS) for functionals depending on a parameter belonging to a real interval and which are the sum of a locally Lipschitz continuous term and of a convex, proper, lower semicontinuous function, is obtained when the parameter runs in a full measure subset of the given interval. Specifically, for this class of non-smooth functions, we obtain BPS related to mountain pass and to global infima levels. This is done by developing a unifying approach, which applies to both cases and relies on a suitable deformation lemma. © 2011 Elsevier Ltd. All rights reserved.

KW - Bounded Palais-Smale sequences

KW - Critical points

KW - Deformation

KW - Mountain pass geometry

KW - Non-smooth functions

UR - http://hdl.handle.net/10447/258508

M3 - Article

VL - 74

SP - 5446

EP - 5454

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

SN - 0362-546X

ER -