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This article shows a stochastic version of the Schauder-Tychonoff fixed-pointtheoren and yields a stochastically weak solution to a large class of systemsof nonlinear reaction-diffusion type equations driven by a cylindrical Wienerprocess and a Poisson random measure with certain moments. The main theoremsolves systems whose reaction terms do not exhibit boundedness, dissipativitynor coercivity conditions.

A Schauder-Tychonoff fixed-point approach for nonlinear L\'evy driven reaction-diffusion systems