Classification of Radial Solutions to Liouville Systems with Singularities
نویسندگان
چکیده
Let A = (aij)n×n be a nonnegative, symmetric, irreducible and invertible matrix. We prove the existence and uniqueness of radial solutions to the following Liouville system with singularity: ∆ui + ∑n j=1 aij |x| βj ej = 0, R2, i = 1, ..., n ∫ R2 |x| βieui(x)dx <∞, i = 1, ..., n where β1, ..., βn are constants greater than −2. If all βis are negative we prove that all solutions are radial and the linearized system is non-degenerate.
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