Eigenvalues and bifurcation for problems with positively homogeneous operators and reaction-diffusion systems with unilateral terms

0482022 - MÚ 2019 RIV GB eng J - Journal Article
Kučera, Milan - Navrátil, J.
Eigenvalues and bifurcation for problems with positively homogeneous operators and reaction-diffusion systems with unilateral terms.
Nonlinear Analysis: Theory, Methods & Applications. Roč. 166, January (2018), s. 154-180. ISSN 0362-546X. E-ISSN 1873-5215
Institutional support: RVO:67985840
Keywords : global bifurcation * maximal eigenvalue * positively homogeneous operators
OECD category: Pure mathematics
Impact factor: 1.450, year: 2018
http://www.sciencedirect.com/science/article/pii/S0362546X17302559?via%3Dihub

Reaction-diffusion systems satisfying assumptions guaranteeing Turing's instability and supplemented by unilateral terms of type v- 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.
Permanent Link: http://hdl.handle.net/11104/0277426