Bifurcation analysis of fractional Kirchhoff–Schrödinger–Poisson systems in R 3

Abstract

In this paper, we investigate the bifurcation results of the fractional Kirchhoff–Schrödinger–Poisson system { M ( [ u ] s 2 ) ( − Δ ) s u + V ( x ) u + ϕ ( x ) u = λ g ( x ) | u | p − 1 u + | u | 2 s ∗ − 2 u i n R 3 , ( − Δ ) t ϕ ( x ) = u 2 i n R 3 , where s , t ∈ ( 0 , 1 ) with 2 t + 4 s > 3 and the potential function V is a continuous function. We show that the existence of components of (weak) solutions of the above equation bifurcates out from the first eigenvalue λ 1 of the problem ( − Δ ) s u + V ( x ) u = λ g ( x ) u in R 3 . The main feature of this paper is the inclusion of a potentially degenerate Kirchhoff model, combined with the critical nonlinearity.