Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
7222722 | Nonlinear Analysis: Theory, Methods & Applications | 2018 | 27 Pages |
Abstract
Reaction-diffusion systems satisfying assumptions guaranteeing Turing's instability and supplemented by unilateral terms of type vâ and v+ are studied. Existence of critical points and sometimes also bifurcation of stationary spatially non-homogeneous solutions are proved for rates of diffusions for which it is excluded without any unilateral term. The main tool is a general result giving a variational characterization of the largest eigenvalue for positively homogeneous operators in a Hilbert space satisfying a condition related to potentiality, and existence of bifurcation for equations with such operators. The originally non-variational (non-symmetric) system is reduced to a single equation with a positively homogeneous potential operator and the abstract results mentioned are used.
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Authors
Milan KuÄera, Josef Navrátil,