Asymptotic behaviour of a semilinear elliptic system with a large exponent
Guerra, Ignacio
Original · EN
Consider the problem eqnarray* -Δu &=& v 2N-2, v>0 in Ω, -Δv &=& uᵖ, u>0 in Ω, u&=&v=0 on ∂ Ω, eqnarray* where Ω is a bounded convex domain in ⁿ, N>2, with smooth boundary ∂ Ω. We study the asymptotic behaviour of the least energy solutions of this system as p→ ∞. We show that the solution remain bounded for p large and have one or two peaks away form the boundary. When one peak occurs we characterize its location.
English translation
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