Positive Solutions of Delta u+u^{(n+2)/(n-2)}=0 on Contractible Domains (Journal of Partial Differential Equations, 2020)
We show that there are bounded contractible domains in R^n, n &#8805 3, on which the Dirichlet problem for the equation &#916u +u^{(n+2)/(n-2)} = 0 admit positive solutions. This result, combining with the well-known nonexistence result of Pohozaev, implies that geometry of the domains plays a crucial role in the solvability of the problem.