Sign-changing Blowing-up Solutions for Supercritical Bahri-coron’s Problem
نویسندگان
چکیده
Let Ω be a bounded domain in Rn, n ≥ 3 with smooth boundary ∂Ω and a small hole. We give the first example of sign-changing bubbling solutions to the nonlinear elliptic problem −∆u = |u| n+2 n−2+ε−1u in Ω, u = 0 on ∂Ω, where ε is a small positive parameter. The basic cell in the construction is the signchanging nodal solution to the critical Yamabe problem −∆w = |w| 4 n−2w, w ∈ D(R) which has large number (3n) of kernels.
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