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. 
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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/

[1] Pokhozhaev S. I., “O sobstvennykh funktsiyakh uravneniya $\Delta u+\lambda f(u)=0$”, DAN SSSR, 165:1 (1965), 36–39 | Zbl

[2] Abduragimov E. I., “O polozhitelnom radialno-simmetricheskom reshenii zadachi Dirikhle dlya odnogo nelineinogo uravneniya i chislennom metode ego polucheniya”, Izv. vuzov. Matematika, 1997, no. 5, 3–6 | MR | Zbl

[3] Na Ts., Vychislitelnye metody resheniya prikladnykh granichnykh zadach, Mir, M., 1982, 296 pp. | MR