Abundance of entire solutions to nonlinear elliptic equations by the variational method

L. M. Lerman, P. E. Naryshkin, A. I. Nazarov

Результат исследований: Научные публикации в периодических изданияхстатья

Выдержка

We study entire bounded solutions to the equation Δu−u+u3=0 in R2. Our approach is purely variational and is based on concentration arguments and symmetry considerations. This method allows us to construct in an unified way several types of solutions with various symmetries (radial, breather type, rectangular, triangular, hexagonal, etc.), both positive and sign-changing. It is also applicable for more general equations in any dimension.

Язык оригиналаанглийский
Номер статьи111590
ЖурналNonlinear Analysis, Theory, Methods and Applications
Том190
Ранняя дата в режиме онлайн17 авг 2019
DOI
СостояниеЭлектронная публикация перед печатью - 17 авг 2019

Отпечаток

Entire Solution
Nonlinear Elliptic Equations
Variational Methods
Radial Symmetry
Breathers
Bounded Solutions
Hexagon
Triangular
Entire
Symmetry

Предметные области Scopus

  • Анализ
  • Прикладная математика

Цитировать

@article{8fb9b2c249264850a3a9562537d66f2f,
title = "Abundance of entire solutions to nonlinear elliptic equations by the variational method",
abstract = "We study entire bounded solutions to the equation Δu−u+u3=0 in R2. Our approach is purely variational and is based on concentration arguments and symmetry considerations. This method allows us to construct in an unified way several types of solutions with various symmetries (radial, breather type, rectangular, triangular, hexagonal, etc.), both positive and sign-changing. It is also applicable for more general equations in any dimension.",
author = "Lerman, {L. M.} and Naryshkin, {P. E.} and Nazarov, {A. I.}",
year = "2019",
month = "8",
day = "17",
doi = "10.1016/j.na.2019.111590",
language = "English",
volume = "190",
journal = "Nonlinear Analysis, Theory, Methods and Applications",
issn = "0362-546X",
publisher = "Elsevier",

}

Abundance of entire solutions to nonlinear elliptic equations by the variational method. / Lerman, L. M.; Naryshkin, P. E.; Nazarov, A. I.

В: Nonlinear Analysis, Theory, Methods and Applications, Том 190, 111590, 01.01.2020.

Результат исследований: Научные публикации в периодических изданияхстатья

TY - JOUR

T1 - Abundance of entire solutions to nonlinear elliptic equations by the variational method

AU - Lerman, L. M.

AU - Naryshkin, P. E.

AU - Nazarov, A. I.

PY - 2019/8/17

Y1 - 2019/8/17

N2 - We study entire bounded solutions to the equation Δu−u+u3=0 in R2. Our approach is purely variational and is based on concentration arguments and symmetry considerations. This method allows us to construct in an unified way several types of solutions with various symmetries (radial, breather type, rectangular, triangular, hexagonal, etc.), both positive and sign-changing. It is also applicable for more general equations in any dimension.

AB - We study entire bounded solutions to the equation Δu−u+u3=0 in R2. Our approach is purely variational and is based on concentration arguments and symmetry considerations. This method allows us to construct in an unified way several types of solutions with various symmetries (radial, breather type, rectangular, triangular, hexagonal, etc.), both positive and sign-changing. It is also applicable for more general equations in any dimension.

UR - http://www.scopus.com/inward/record.url?scp=85070685073&partnerID=8YFLogxK

UR - http://www.mendeley.com/research/abundance-entire-solutions-nonlinear-elliptic-equations-variational-method

U2 - 10.1016/j.na.2019.111590

DO - 10.1016/j.na.2019.111590

M3 - Article

AN - SCOPUS:85070685073

VL - 190

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

SN - 0362-546X

M1 - 111590

ER -