Positive solutions of Δu+usup(n+2)-(n-2)-sup=0 on contractible domains PDF
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Preview Positive solutions of Δu+usup(n+2)-(n-2)-sup=0 on contractible domains
Description:
We show that there are bounded contractible domains in Rn, n ≥ 3, on which the Dirichlet problem for the equation Δu+u(u+2)/(u-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.
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