Multiplicity results for fractional Laplace problems with critical growth

This paper deals with multiplicity and bifurcation results for nonlinear problems driven by the fractional Laplace operator $(-Δ)^s$ and involving a critical Sobolev term. In particular, we consider $$\begin{cases} (-Δ)^su=γ|u|^{2^*-2}u+f(x,u) & \mbox{in } Ωu=0 & \mbox{in } \mathbb R^n\setminus Ω, \end{cases}$$ where $Ω\subset\mathbb R^n$ is an open bounded set with continuous boundary, $n>2s$ with $s\in(0,1)$, $γ$ is a positive real parameter, $2^*=2n/(n-2s)$ is the fractional critical Sobolev exponent and $f$ is a Carathéodory function satisfying different subcritical conditions.

No reviews yet.

No comments yet.