Positive or sign-changing solutions for a critical semilinear nonlocal equation (Q322097)

The authors consider the following critical semilinear nonlocal equation involving the fractional Laplacian. \[ (-\Delta)^s u=K(|x|)|u|^{2^*_s-2}u\quad\text{in }\mathbb R^N, \] where \(K(|x|)\) is a positive radial function, \(N>2+2s,\) \(0<s<1,\) and \(2^*_s={{2N}\over{N-2_s}}\). Under some asymptotic assumptions on \(K(x)\) at an extreme point, it is proved that the problem has infinitely many nonradial positive or sign-changing solutions.