Bifurcation problems for double critical Schrodinger-Poisson systems

This paper focuses on the following double critical Schrödinger-Poisson system [Formula: see text] where [Formula: see text] and [Formula: see text] is a nonnegative weight function. Moreover, by the celebrated global bifurcation theorem due to Rabinowitz [37], we prove existence of (weak) solutions for the above system. To the best of our knowledge, it seems to be the first time contribution to considering the bifurcation and existence of solutions for Schrödinger-Poisson systems with doubly critical growth by the global bifurcation theorem [37]. To some extent, our main theorems complement some results established in [28, 29, 32, 33, 43].