[Author]
 Nazarov, A. I.; Shcheglova, A. P.

[Title]
 Solution with various structures for semilinear equations in $\mathbb R^n$
 driven by fractional Laplacian

[AMS Subj-class]
 35R11 Fractional partial differential equations
 35B06 Symmetries, invariants, etc. in context of PDEs
 35J20 Variational methods for second-order elliptic equations

[Keywords]
 fractional Laplacians, semilinear equations, periodic structures, 
 breather solutions

[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, quasiperiodic, breather type, etc.).

[Comments]
 LaTeX, Russian, 28 pp.

[Contact e-mail]
 al.il.nazarov@gmail.com