LAUSR

In this paper we study some nonlinear elliptic equations in $${\mathbb R}^n$$Rn obtained as a perturbation of the problem with the fractional critical Sobolev exponent, that is $$\begin{aligned} (-\Delta )^s u = \varepsilon \,h\,u_+^q + u_+^p \ { \text{ in } }{\mathbb R}^n, \end{aligned}$$(-Δ)su=εhu+q+u+pinRn,where $$s\in (0,1)$$s∈(0,1), $$n>4s$$n>4s, $$\varepsilon >0$$ε>0 is a small parameter, $$p=\frac{n+2s}{n-2s}$$p=n+2sn-2s, $$0