标题： 半线性方程在$\mathbb R^n$中的各种结构解，由分数拉普拉斯算子驱动 显示英文标题

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

摘要： 我们研究分数方程$(-\Delta)^s u + u - |u|^{q-2}u = 0$在$\mathbb R^n$中对于$n\ge2$和次临界指数$q>2$的有界解。 应用基于集中论证和对称性考虑的变分方法，该方法由 Lerman, Naryshkin 和 Nazarov (2020) 引入，我们构造了几种具有不同结构（径向、矩形、三角形、六边形、准周期、呼吸子型等）的解。 显示英文摘要

摘要： 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.).