(untitled) (Journal of Partial Differential Equations, 2018)
We consider the following nonlinear problem -Δu=u^N+2N-2 , u > 0, in R^N\Ω, u(x)→ 0, as |x|→+∞, ∂u∂n=0, on ∂Ω, where Ω⊂R^N N ≥ 4 is a smooth and bounded domain and n denotes inward normal vector of ∂Ω. We prove that the above problem has infinitely many solutions whose energy can be made arbitrarily large when Ω is convex seen from inside (with some symmetries).