## Qualitative properties of ground states for singular elliptic equations with weights.(English)Zbl 1115.35050

In this work, the authors deal with non-negative radial solutions of the singular quasilinear elliptic PDE $\text{div}(g(|x|)|\nabla u|^{m-2}\nabla u)+h(|x|)f(u)=0, \;x\in \mathbb R^n \setminus\{0\},$ where $$g,h:\mathbb R^+\to \mathbb R^+$$, $$f\in C(\mathbb R^+)\cap L^1(0,1)$$, $$m>1$$ and $$n\geq 1$$. The singularities can appear in the functions $$g, h$$ and $$f$$ at the origin. This class contains (among other models) the generalized Matukuma equation.
The main theorems are devoted to establishing the uniqueness of ground states for such spatially dependent PDE under different conditions.

### MSC:

 35J60 Nonlinear elliptic equations 35J70 Degenerate elliptic equations 35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
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