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

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

Research output

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.

Original languageEnglish
Article number111590
JournalNonlinear Analysis, Theory, Methods and Applications
Volume190
Early online date17 Aug 2019
DOIs
Publication statusE-pub ahead of print - 17 Aug 2019

Fingerprint

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

Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

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