On Schrödinger–Poisson systems involving concave–convex nonlinearities via a novel constraint approach

In this paper, we investigate the multiplicity of positive solutions for a class of Schrödinger–Poisson systems with concave and convex nonlinearities as follows: [Formula: see text] where [Formula: see text] are two parameters, [Formula: see text], [Formula: see text] is a potential well, [Formula: see text] and [Formula: see text]. Such problem cannot be studied by applying variational methods in a standard way, since the (PS) condition is still unsolved on [Formula: see text] due to [Formula: see text]. By developing a novel constraint approach, we prove that the above problem admits at least two positive solutions.