Classification of radial solutions to Liouville systems with singularities
Copyright policy )Classification of radial solutions to Liouville systems with singularities
Let $A=(a_{ij})_{n\times n}$ be a nonnegative, symmetric, irreducible and invertible matrix. We prove the existence and uniqueness of radial solutions to the following Liouville system with singularity: $$\{{array}{ll} Δu_i+\sum_{j=1}^n a_{ij}|x|^{β_j}e^{u_j(x)}=0,\quad \mathbb R^2, \quad i=1,...,n \int_{\mathbb R^2}|x|^{β_i}e^{u_i(x)}dx
25 pages
- Florida State University United States
- University of Florida United States
- University of Alabama at Birmingham United States
radial symmetry, Nonlinear elliptic equations, non-degeneracy, singularity, Mathematics - Analysis of PDEs, Second-order elliptic systems, classification of solutions, FOS: Mathematics, Singular elliptic equations, Liouville system, 35J60, 35J55, Analysis of PDEs (math.AP)
radial symmetry, Nonlinear elliptic equations, non-degeneracy, singularity, Mathematics - Analysis of PDEs, Second-order elliptic systems, classification of solutions, FOS: Mathematics, Singular elliptic equations, Liouville system, 35J60, 35J55, Analysis of PDEs (math.AP)
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