Geodesic
Uniqueness of a positive radially symmetric solution in a ball to the Dirichlet problem for one nonlinear differential equation of the second order
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2008), pp. 3-6

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In the ball $S=\{x\in R^n:|x|1\}$ ($n\ge3$) with the boundary $\Gamma$ we consider the Dirichlet problem \begin{gather*} \Delta u+|x|^m|u|^p=0, \quad x\in S, \\ u_\Gamma=0, \end{gather*} where $m\ge0$, $p>1$ are constants. We prove that the problem has a unique positive radially symmetric solution.
Mots-clés : positive solution
Keywords: radially symmetric solution, Dirichlet problem, differential equation. 
@article{IVM_2008_12_a0,
     author = {E. I. Abduragimov},
     title = {Uniqueness of a positive radially symmetric solution in a ball to the {Dirichlet} problem for one nonlinear differential equation of the second order},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {3--6},
     publisher = {mathdoc},
     number = {12},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2008_12_a0/}
}
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E. I. Abduragimov. Uniqueness of a positive radially symmetric solution in a ball to the Dirichlet problem for one nonlinear differential equation of the second order. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2008), pp. 3-6. http://geodesic.mathdoc.fr/item/IVM_2008_12_a0/