Infinitely many solutions for Schrödinger–Newton equations

Source abstract

We prove the existence of infinitely many non-radial positive solutions for the Schrödinger–Newton system [Formula: see text] provided that [Formula: see text] has the following behavior at infinity: [Formula: see text] where [Formula: see text] and [Formula: see text] are some positive constants. In particular, for any [Formula: see text] large we use a reduction method to construct [Formula: see text]-bump solutions lying on a circle of radius [Formula: see text].