Sign changing bubbling solutions for a critical Neumann problem in 3D. (November 2019) - Salazar, Dora
Abstract: Let Ω be a smooth bounded domain in R 3 . We consider the problem Δ u − λ u + | u | 4 u = 0 in Ω, with zero Neumann boundary conditions, and investigate the existence of sign changing solutions, which concentrate simultaneously around k different points of Ω as λ approaches a special value λ 0 . We characterize the number λ 0 in terms of the Green function of − Δ + λ . In particular, we construct a family of solutions exhibiting bubbling behavior at two different points of an annular domain as λ tends to λ 0 . In doing so, we also derive a representation formula of the Green function of − Δ with Neumann boundary conditions in the annulus in terms of zonal harmonics.