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
СостояниеОпубликовано - 1 янв 2020

Отпечаток

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

Предметные области Scopus

  • Анализ
  • Прикладная математика

Цитировать

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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

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

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AU - Naryshkin, P. E.

AU - Nazarov, A. I.

PY - 2020/1/1

Y1 - 2020/1/1

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.

KW - POSITIVE SOLUTIONS

KW - NONUNIFORM SYSTEM

KW - WAVE-SOLUTIONS

KW - FREE-ENERGY

KW - EXISTENCE

KW - ATTRACTORS

KW - MANIFOLDS

KW - PRINCIPLE

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DO - 10.1016/j.na.2019.111590

M3 - Article

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JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

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