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A nonlinear elliptic problem with a complex spectrum of solutions. (English. Russian original) Zbl 0619.35043
U.S.S.R. Comput. Math. Math. Phys. 26, No. 2, 48-54 (1986); translation from Zh. Vychisl. Mat. Mat. Fiz. 26, No. 3, 398-407 (1986).
The authors consider the radial-symmetric positive solution of the nonlinear elliptic equation in \({\mathbb{R}}^ N\) arising from the study of the unbounded automodel solutions of the quasilinear parabolic equation with the source \[ u_ t=\nabla (| \nabla u|^{\sigma}\nabla u)+u^{\beta},\quad t>0,\quad x\in {\mathbb{R}}^ N,\quad \sigma,\beta \in R,\quad \sigma >0,\quad \beta >\sigma +1. \] It is shown that the elliptic problem has 4 different families of solutions; three discrete (denumerable) solutions and one continual solution. In the one- dimensional case the solutions are constructed numerically, the bifurcation situation is given.
Reviewer: Ya.A.Rojtberg

MSC:
35J60 Nonlinear elliptic equations
35K55 Nonlinear parabolic equations
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