A Schauder-Tychonoff fixed-point approach for nonlinear Lévy driven reaction-diffusion systems

Abstract: This article shows a stochastic version of the Schauder-Tychonoff fixed-point theoren and yields a stochastically weak solution to a large class of systems of nonlinear reaction-diffusion type equations driven by a cylindrical Wiener process and a Poisson random measure with certain moments. The main theorem solves systems whose reaction terms do not exhibit boundedness, dissipativity nor coercivity conditions.