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

We study bounded solutions to the fractional equation (-Δ )^s u+u-|u|^q-2u=0 in ℝ^n for n≥ 2 and subcritical exponent q>2 . Applying the variational approach based on concentration arguments and symmetry considerations which was introduced by Lerman, Naryshkin, Nazarov (Nonlinear Anal. 190:111590, 2020) we construct several types of solutions with various structures (radial, rectangular, triangular, hexagonal, quasi-periodic, breather type, etc.).