Asymptotic behaviour of positive solutions for critical systems with strongly indefinite structure

Abstract

In this article, we study the asymptotic behaviour of positive solutions to the Hamiltonian elliptic systems −Δv = u ^p−ϵ, −Δu = v ^q−δ in Ω; u, v > 0 in Ω; u = v = 0 on ∂Ω, where Ω is a unit ball in R ^N (N ≥ 3) centered at the origin; . The solutions are shown to blow up at exactly the origin. The exact rate of blowing up is also given.

Keywords:

• Hamiltonian systems
• Green's function
• asymptotic behaviour
• ground state

Acknowledgements

The second author is partially supported by the Key Project of the National Natural Science Foundation (No. 10631030) and the Special Excellent Dissertation Fund of the Chinese Academy of Sciences, China.