Solutions with various structures for semilinear equations in $\mathbb R^n$ driven by fractional Laplacian

A. I. Nazarov; A. P. Shcheglova

Solutions with various structures for semilinear equations in $\mathbb R^n$ driven by fractional Laplacian

Analysis of PDEs 2021-11-16 v1

Authors: A. I. Nazarov , A. P. Shcheglova

Abstract

We study bounded solutions to the fractional equation $(-\Delta)^s u + u - |u|^{q-2}u = 0$ in $\mathbb R^n$ for $n\ge2$ and subcritical exponent $q>2$ . Applying the variational approach based on concentration arguments and symmetry considerations which was introduced by Lerman, Naryshkin and Nazarov (2020) we construct several types of solutions with various structures (radial, rectangular, triangular, hexagonal, quasi-periodic, breather type, etc.).

Keywords

fractional laplacian semilinear equations bounded solutions variational method concentration arguments symmetry breather solutions

Cite

@article{arxiv.2111.07301,
  title  = {Solutions with various structures for semilinear equations in $\mathbb R^n$ driven by fractional Laplacian},
  author = {A. I. Nazarov and A. P. Shcheglova},
  journal= {arXiv preprint arXiv:2111.07301},
  year   = {2021}
}

Comments

28 pages, 21 figures

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