Multiplicity of positive solutions for a fractional Laplacian equations involving critical nonlinearity

Le résumé fourni par la source

In this paper we deal with the multiplicity of positive solutions to the fractional Laplacian equation \begin{equation*} (-Δ)^{\fracα{2}} u=λf(x)|u|^{q-2}u+|u|^{2^{*}_α-2}u, \quad\text{in}\,\,Ω, u=0,\text{on}\,\,\partialΩ, \end{equation*} where $Ω\subset \mathbb{R}^{N}(N\geq 2)$ is a bounded domain with smooth boundary, $00$ such that the problem has at least two positive solutions for each $λ\in (0\,,\,λ_{*})$. In addition, the concentration behavior of the solutions are investigated.

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