2002 Characterizing the existence of large solutions for a class of sublinear problems with nonlinear diffusion
Manuel Delgado, Julián López-Gómez, Antonio Suárez
Adv. Differential Equations 7(10): 1235-1256 (2002). DOI: 10.57262/ade/1356651636


In this paper we characterize the existence of large solutions for a general class of sublinear elliptic problems of logistic type related to the porous media equation. Our main result shows that large solutions do exist if, and only if, the nonlinear diffusion is not too large. As a byproduct of the general theory developed by the authors in [3], those large solutions must be unstable with respect to the positive solutions of the parabolic counterpart of the elliptic model. This seems to be the first result of this nature available in the literature. Most precisely, as the diffusion becomes non-linear the metasolutions become unstable, so arising a classical steady-state gaining the stability lost by the metasolution. In particular, a dynamical bifurcation occurs from the linear diffusion case.


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Manuel Delgado. Julián López-Gómez. Antonio Suárez. "Characterizing the existence of large solutions for a class of sublinear problems with nonlinear diffusion." Adv. Differential Equations 7 (10) 1235 - 1256, 2002. https://doi.org/10.57262/ade/1356651636


Published: 2002
First available in Project Euclid: 27 December 2012

zbMATH: 1207.35133
MathSciNet: MR1919703
Digital Object Identifier: 10.57262/ade/1356651636

Primary: 35J60
Secondary: 35J65 , 35K57

Rights: Copyright © 2002 Khayyam Publishing, Inc.


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Vol.7 • No. 10 • 2002
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