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

DOI10.1007/S00526-023-02453-2arXiv2111.07301MaRDI QIDQ6383000

Alexandra P. Shcheglova, A. I. Nazarov

Publication date: 14 November 2021

Abstract: We study bounded solutions to the fractional equation

(- D e l t a)^{s} u + u - | u |^{q - 2} u = 0

in

m a t h b b R^{n}

for

n g e 2

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.).

Mathematics Subject Classification ID

Almost and pseudo-almost periodic solutions to PDEs (35B15) Variational methods for second-order elliptic equations (35J20) Semilinear elliptic equations (35J61) Fractional partial differential equations (35R11) Symmetries, invariants, etc. in context of PDEs (35B06)

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