Abstract
We study the following boundary value problem (0.1){Δu+λa(x)up−1eup=0,u>0inΩ;u=0on∂Ω, where Ω is a bounded domain in R2 with smooth boundary, λ>0 is a small parameter, the function a(x)≥0 is a smooth potential, and the exponent p satisfies 0<p<2. We construct a family of solutions to problem (0.1) which blows up, as λ→0, at some points of Ω which stay outside the zero set of a(x). We relate the number of possible blow-up points with the zero set of a(x).
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