A Schauder–Tychonoff fixed-point approach for nonlinear Lévy driven reaction–diffusion systems
Abstract
We show a stochastic version of the Schauder-Tychonoff fixed point theorem which yields a solution of the martingale problem for a class of systems of nonlinear reaction-diffusion equations driven by a cylindrical Wiener process and a Poisson random measure with certain moments. By this type of theorem one can solve systems by linearization which have a possibly unbounded, non-dissipative and non-coercive nonlinearity.
Fields of Study & Subjects
Nonlinear Differential Equations Analysis
Stochastic processes and statistical mechanics
Mathematical and Theoretical Epidemiology and Ecology Models
Publication details
- Journal / source
- Stochastics
- Volume
- 98
- Issue
- 5
- Pages
- 730–777
- Publication date
- 29 January 2026
- Language
- EN