A stochastic Schauder-Tychonoff type theorem and its applications

Erika Hausenblas; Ankit Kumar; Jonas M. Tölle

doi:10.1007/s13324-026-01262-y

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arXiv · 2602.17285

A stochastic Schauder-Tychonoff type theorem and its applications

Erika Hausenblas·Ankit Kumar·Jonas M. Tölle

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Abstract

One standard way to prove existence for deterministic, highly nonlinear PDEs is to use the Schauder-Tychonoff fixed-point theorem. In what follows, we introduce and verify a stochastic variant of the Schauder-Tychonoff theorem. We apply our existence result to nonlinear stochastic diffusion equations with non-Lipschitz perturbations

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Erika Hausenblas, Ankit Kumar, Jonas M. Tölle. 2026-02-19. A stochastic Schauder-Tychonoff type theorem and its applications. https://doi.org/10.1007/s13324-026-01262-y

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