A A Study of Semilinear Elliptic Triharmonic Equations Involving Singular Potentials

Abstract

The purpose of this work is to investigate the existence and nonexistence of solutions for the following semilinear sixth-order elliptic problem with a singular potential



-∆3v - µ α

|x|3 v = g(v) + λh(x) in Ω,

v > 0 v = ∆v = ∆2v = 0 in Ω,on ∂Ω,

where Ω ⊂ RN(N ≥ 7) is a smooth bounded domain. ∆3v = ∆(∆2v) , h, g are nonnegative functions.

h ∈ L2(Ω), h ̸≡ 0. µ, λ are positive parameters.