Multiple radial solutions for a class of elliptic systems with singular nonlinearities. (English) Zbl 0954.35054
Summary: We study radial solutions \(u= (u_1,u_2)\) is an exterior domain of \(\mathbb{R}^N\) \((N\geq 3)\) of the elliptic system \(-\Delta u+ V'(u)= 0\), where \(V\) is a positive and singular potential. We look for solutions which satisfy Dirichlet boundary conditions and vanish at infinity. We prove existence of infinitely many radial solutions, which can be topologically classified by their winding numbers around the singularity of \(V\). Furthermore, we study some qualitative properties of such solutions.
MSC:
| 35J50 | Variational methods for elliptic systems |
| 35A05 | General existence and uniqueness theorems (PDE) (MSC2000) |
| 35B65 | Smoothness and regularity of solutions to PDEs |
| 55M25 | Degree, winding number |
| 35R05 | PDEs with low regular coefficients and/or low regular data |
Keywords:
exterior domain; Dirichlet boundary conditions; infinitely many radial solutions; qualitative propertiesReferences:
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