On the existence of infinitely many solutions for a class of semilinear elliptic equations in R N

Francesca Alessio; Paolo Caldiroli; Piero Montecchiari

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1998)

  • Volume: 9, Issue: 3, page 157-165
  • ISSN: 1120-6330

Abstract

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We show, by variational methods, that there exists a set A open and dense in a L R N : a 0 such that if a A then the problem - u + u = a x u p - 1 u , u H 1 R N , with p subcritical (or more general nonlinearities), admits infinitely many solutions.

How to cite

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Alessio, Francesca, Caldiroli, Paolo, and Montecchiari, Piero. "On the existence of infinitely many solutions for a class of semilinear elliptic equations in \( \mathbb{R}^{N} \)." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 9.3 (1998): 157-165. <http://eudml.org/doc/252422>.

@article{Alessio1998,
abstract = {We show, by variational methods, that there exists a set \( \mathcal\{A\} \) open and dense in \( \{a \in L^\{\infty\} ( \mathbb\{R\}^\{N\}) : a \ge 0\} \) such that if \( a \in \mathcal\{A\} \) then the problem \( - \triangle u + u = a(x) |u|^\{p-1\} u, u \in H^\{1\}(\mathcal\{R\}^\{N\}) \), with \( p \) subcritical (or more general nonlinearities), admits infinitely many solutions.},
author = {Alessio, Francesca, Caldiroli, Paolo, Montecchiari, Piero},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Semilinear elliptic equations; Locally compact case; Minimax arguments; Multiplicity of solutions; Genericity; locally compact case; minimax arguments},
language = {eng},
month = {9},
number = {3},
pages = {157-165},
publisher = {Accademia Nazionale dei Lincei},
title = {On the existence of infinitely many solutions for a class of semilinear elliptic equations in \( \mathbb\{R\}^\{N\} \)},
url = {http://eudml.org/doc/252422},
volume = {9},
year = {1998},
}

TY - JOUR
AU - Alessio, Francesca
AU - Caldiroli, Paolo
AU - Montecchiari, Piero
TI - On the existence of infinitely many solutions for a class of semilinear elliptic equations in \( \mathbb{R}^{N} \)
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1998/9//
PB - Accademia Nazionale dei Lincei
VL - 9
IS - 3
SP - 157
EP - 165
AB - We show, by variational methods, that there exists a set \( \mathcal{A} \) open and dense in \( {a \in L^{\infty} ( \mathbb{R}^{N}) : a \ge 0} \) such that if \( a \in \mathcal{A} \) then the problem \( - \triangle u + u = a(x) |u|^{p-1} u, u \in H^{1}(\mathcal{R}^{N}) \), with \( p \) subcritical (or more general nonlinearities), admits infinitely many solutions.
LA - eng
KW - Semilinear elliptic equations; Locally compact case; Minimax arguments; Multiplicity of solutions; Genericity; locally compact case; minimax arguments
UR - http://eudml.org/doc/252422
ER -

References

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