This article is cited in 2 papers

Method of monotone solutions for reaction-diffusion equations

V. Volpert^abc, V. Vougalter<sup>d

a</sup> Institut Camille Jordan, UMR 5208 CNRS, University Lyon 1, 69622 Villeurbanne, France
^b INRIA Team Dracula, INRIA Lyon La Doua, 69603 Villeurbanne, France
^c RUDN University, 6 Miklukho-Maklaya st., 117198 Moscow, Russia
^d Department of Mathematics, University of Toronto, Toronto, M5S 2E4 Ontario, Canada

Abstract: Existence of solutions of reaction-diffusion systems of equations in unbounded domains is studied by the Leray–Schauder (LS) method based on the topological degree for elliptic operators in unbounded domains and on a priori estimates of solutions in weighted spaces. We identify some reactiondiffusion systems for which there exist two subclasses of solutions separated in the function space, monotone and non-monotone solutions. A priori estimates and existence of solutions are obtained for monotone solutions allowing to prove their existence by the LS method. Various applications of this method are given.

UDC: 517.98

DOI: 10.22363/2413-3639-2017-63-3-437-454