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Pucci, Patrizia; García-Huidobro, Marta; Manásevich, Raúl; Serrin, James

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

Ann. Mat. Pura Appl. (4) 185, Suppl. 5, S205-S243 (2006).
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.
Reviewer: Luis Alberto Fernandez (Santander)

Cited in 24 Documents

MSC:

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

Keywords:

ground states; \(m\)-Laplacian operator; weight functions; uniqueness
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\textit{P. Pucci} et al., Ann. Mat. Pura Appl. (4) 185, S205--S243 (2006; Zbl 1115.35050)
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