Displaying similar documents to “Explosive solutions of semilinear elliptic systems with gradient term.”

A note on nonexistence of radial solutions to semilinear elliptic inequations.

Mohammed Guedda (2002)

Publicacions Matemàtiques

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We study the nonexistence result of radial solutions to -Δu + c u/(|x|) + |x||u|u ≤ 0 posed in B or in B {0} where B is the unit ball centered at the origin in R, N ≥ 3. Moreover, we give a complete classification of radial solutions to the problem -Δu + c u/(|x|) + |x||u|u = 0. In particular we prove that the latter has exactly one family of radial solutions.

Existence and nonexistence of radial positive solutions of superlinear elliptic systems.

Abdelaziz Ahammou (2001)

Publicacions Matemàtiques

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The main goal in this paper is to prove the existence of radial positive solutions of the quasilinear elliptic system ⎧ -Δpu = f(x,u,v) in Ω, ⎨ -Δqv = g(x,u,v) in Ω, ⎩ u = v = 0 on ∂Ω, where Ω is a ball in RN and f, g are positive continuous functions satisfying f(x, 0, 0) = g(x, 0, 0) = 0 and some growth conditions which correspond, roughly...

The waiting time property for parabolic problems trough the nondiffusion of support for the stationary problems.

Luis Alvarez, Jesús Ildefonso Díaz (2003)

RACSAM

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In this note we study the waiting time phenomenon for local solutions of the nonlinear diffusion equation through its connection with the nondiffusion of the support property for local solutions of the family of discretized elliptic problems. We show that, under a suitable growth condition on the initial datum near the boundary of its support, a finite part of the family of solutions of the discretized problem maintain unchanged its support.