In this paper, we study the higher order conformally covariant equation (- Δ)n/2 w = (n - 1)!enw x ∈ Rn for all even dimensions n. Let a = 1/|Sn| ∫Rn enw dx. We prove, for every 0 < a < 1, the existence of at least one solution. In particular, for n = 4, we obtain the existence of radial solutions.
All Science Journal Classification (ASJC) codes
- Discrete Mathematics and Combinatorics
- Applied Mathematics
- Conformally covariant equations
- Higher order semilinear elliptic equations
- Variational method