Linking solutions for quasilinear equations at critical growth involving the "1-Laplace" operator

Marco Degiovanni; Paola Magrone

doi:10.1007/s00526-009-0246-1

Linking solutions for quasilinear equations at critical growth involving the "1-Laplace" operator

Marco Degiovanni^*
, Paola Magrone

^*Autore corrispondente per questo lavoro

Facoltà di Scienze Matematiche, Fisiche e Naturali

Roma Tre University

Risultato della ricerca: Contributo in rivista › Articolo › peer review

18 Citazioni (Scopus)

Abstract

We show that the problem at critical growth, involving the 1-Laplace operator and obtained by relaxation of\r\n-\Delta_1 u=\lambda |u|^{-1}u + |u|^{1^*-2} u,\r\nadmits a nontrivial solution u in BV(\Omega) for any \lambda\geq\lambda_1.\r\nNonstandard linking structures, for the associated functional, are recognized.

Lingua originale	Inglese
pagine (da-a)	591-609
Numero di pagine	19
Rivista	Calculus of Variations and Partial Differential Equations
Volume	36
Numero di pubblicazione	4
DOI	https://doi.org/10.1007/s00526-009-0246-1
Stato di pubblicazione	Pubblicato - 2009

All Science Journal Classification (ASJC) codes

Analisi
Matematica Applicata

Keywords

Critical point theory
Differential equations
Equazioni differenziali
Teoria dei punti critici

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10.1007/s00526-009-0246-1

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title = "Linking solutions for quasilinear equations at critical growth involving the {"}1-Laplace{"} operator",

abstract = "We show that the problem at critical growth, involving the 1-Laplace operator and obtained by relaxation of\textbackslash{}r\textbackslash{}n-\textbackslash{}Delta\_1 u=\textbackslash{}lambda |u|\textasciicircum{}\{-1\}u + |u|\textasciicircum{}\{1\textasciicircum{}*-2\} u,\textbackslash{}r\textbackslash{}nadmits a nontrivial solution u in BV(\textbackslash{}Omega) for any \textbackslash{}lambda\textbackslash{}geq\textbackslash{}lambda\_1.\textbackslash{}r\textbackslash{}nNonstandard linking structures, for the associated functional, are recognized.",

keywords = "Critical point theory, Differential equations, Equazioni differenziali, Teoria dei punti critici, Critical point theory, Differential equations, Equazioni differenziali, Teoria dei punti critici",

author = "Marco Degiovanni and Paola Magrone",

year = "2009",

doi = "10.1007/s00526-009-0246-1",

language = "English",

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pages = "591--609",

journal = "Calculus of Variations and Partial Differential Equations",

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TY - JOUR

T1 - Linking solutions for quasilinear equations at critical growth involving the "1-Laplace" operator

AU - Degiovanni, Marco

AU - Magrone, Paola

PY - 2009

Y1 - 2009

N2 - We show that the problem at critical growth, involving the 1-Laplace operator and obtained by relaxation of\r\n-\Delta_1 u=\lambda |u|^{-1}u + |u|^{1^*-2} u,\r\nadmits a nontrivial solution u in BV(\Omega) for any \lambda\geq\lambda_1.\r\nNonstandard linking structures, for the associated functional, are recognized.

AB - We show that the problem at critical growth, involving the 1-Laplace operator and obtained by relaxation of\r\n-\Delta_1 u=\lambda |u|^{-1}u + |u|^{1^*-2} u,\r\nadmits a nontrivial solution u in BV(\Omega) for any \lambda\geq\lambda_1.\r\nNonstandard linking structures, for the associated functional, are recognized.

KW - Critical point theory

KW - Differential equations

KW - Equazioni differenziali

KW - Teoria dei punti critici

KW - Critical point theory

KW - Differential equations

KW - Equazioni differenziali

KW - Teoria dei punti critici

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SN - 0944-2669

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JO - Calculus of Variations and Partial Differential Equations

JF - Calculus of Variations and Partial Differential Equations

IS - 4

ER -

Linking solutions for quasilinear equations at critical growth involving the "1-Laplace" operator

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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