Fractional Schrodinger-Poisson systems with weighted Hardy potential and critical exponent

Abstract

In this article we consider the fractional Schrodinger-Poisson system $$\displaylines{ (-\Delta)^{s} u - \mu \frac{\Phi(x/|x|)}{|x|^{2s}} u +\lambda \phi u = |u|^{2^*_s-2}u,\quad \text{in } \mathbb{R}^3,\cr (-\Delta)^t \phi = u^2, \quad \text{in } \mathbb{R}^3, }$$ where \(s\in(0,3/4)\), \(t\in(0,1)\), \(2t+4s=3\), \(\lambda>0\) and \(2^*_s=6/(3-2s)\) is the Sobolev critical exponent. By using perturbation method, we establish the existence of a solution for \(\lambda\) small enough. For more information see https://ejde.math.txstate.edu/Volumes/2020/01/abstr.html

Multiple positive solutions to the fractional Kirchhoff problem with critical indefinite nonlinearities

“…Xie-Chen [26] presented a multiplicity result on the Kirchhoff-type problems in the bounded domain by using a similar strategy. A number of works dealt with the fractional differential equations [3,6,7,11,21] and some recent results on problem (1.3) can be seen in [4,5,10,12,13,14,15,16,22,23,27] and the references therein.…”