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.