Standard

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

In: Nonlinear Analysis, Theory, Methods and Applications, Vol. 190, 111590, 01.01.2020.

Research output: Contribution to journal › Article › peer-review

Harvard

Lerman, LM, Naryshkin, PE & Nazarov, AI 2020, 'Abundance of entire solutions to nonlinear elliptic equations by the variational method', Nonlinear Analysis, Theory, Methods and Applications, vol. 190, 111590. https://doi.org/10.1016/j.na.2019.111590

APA

Lerman, L. M., Naryshkin, P. E., & Nazarov, A. I. (2020). Abundance of entire solutions to nonlinear elliptic equations by the variational method. Nonlinear Analysis, Theory, Methods and Applications, 190, [111590]. https://doi.org/10.1016/j.na.2019.111590

Vancouver

Lerman LM, Naryshkin PE, Nazarov AI. Abundance of entire solutions to nonlinear elliptic equations by the variational method. Nonlinear Analysis, Theory, Methods and Applications. 2020 Jan 1;190. 111590. https://doi.org/10.1016/j.na.2019.111590

Author

Lerman, L. M. ; Naryshkin, P. E. ; Nazarov, A. I. / Abundance of entire solutions to nonlinear elliptic equations by the variational method. In: Nonlinear Analysis, Theory, Methods and Applications. 2020 ; Vol. 190.

BibTeX

@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.",
keywords = "POSITIVE SOLUTIONS, NONUNIFORM SYSTEM, WAVE-SOLUTIONS, FREE-ENERGY, EXISTENCE, ATTRACTORS, MANIFOLDS, PRINCIPLE",
author = "Lerman, {L. M.} and Naryshkin, {P. E.} and Nazarov, {A. I.}",
note = "Publisher Copyright: {\textcopyright} 2019 Elsevier Ltd",
year = "2020",
month = jan,
day = "1",
doi = "10.1016/j.na.2019.111590",
language = "English",
volume = "190",
journal = "Nonlinear Analysis, Theory, Methods and Applications",
issn = "0362-546X",
publisher = "Elsevier",

}

RIS

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.

N1 - Publisher Copyright: © 2019 Elsevier Ltd

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

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 -

ID: 45872378