Construction of infinitely many sign-changing solutions for the Hartree type Brezis–Nirenberg problem

In this paper, we study the following problem: −Δu=∫Ω|u(z)|2|y−z|4dzu+λu, in Ω, u=0, on ∂Ω, where Ω is a bounded domain in R6. If λ > 0 is small, the single bubbling solution of the above problem has been constructed in Yang et al. [J. Differ. Equations 344, 260–324 (2023)]. We first prove that this solution is non-degenerate. Then, using this result and the finite dimensional reduction argument, we prove that if Ω is a ball, the above problem has infinitely many sign-changing bubbling solutions, whose energy can be arbitrarily large.