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

Erika Hausenblas; Michael A. Högele; Kistosil Fahim

doi:10.1080/17442508.2025.2605337

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

Erika Hausenblas^*
, Michael A. Högele
, Kistosil Fahim

^*Corresponding author for this work

Department Mathematik und Informationstechnologie
University of Leoben
Departamento de Matemáticas
Universidad de los Andes Colombia

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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 by linearization systems which have a possibly unbounded, non-dissipative and non-coercive nonlinearity.

Original language	English
Pages (from-to)	730-777
Number of pages	48
Journal	Stochastics
Volume	98
Issue number	5
DOIs	https://doi.org/10.1080/17442508.2025.2605337
Publication status	Published - 2026

Keywords

Stochastic Schauder–Tychonoff type theorem
nonlinear stochastic partial differential equation

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10.1080/17442508.2025.2605337

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title = "A Schauder{\textendash}Tychonoff fixed-point approach for nonlinear L{\'e}vy driven reaction{\textendash}diffusion systems",

abstract = "We show a stochastic version of the Schauder{\textendash}Tychonoff fixed point theorem which yields a solution of the martingale problem for a class of systems of nonlinear reaction{\textendash}diffusion equations driven by a cylindrical Wiener process and a Poisson random measure with certain moments. By this type of theorem one can solve by linearization systems which have a possibly unbounded, non-dissipative and non-coercive nonlinearity.",

keywords = "Stochastic Schauder{\textendash}Tychonoff type theorem, nonlinear stochastic partial differential equation",

author = "Erika Hausenblas and H{\"o}gele, \{Michael A.\} and Kistosil Fahim",

note = "Publisher Copyright: {\textcopyright} 2026 The Author(s). Published by Informa UK Limited, trading as Taylor \& Francis Group.",

year = "2026",

doi = "10.1080/17442508.2025.2605337",

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T1 - A Schauder–Tychonoff fixed-point approach for nonlinear Lévy driven reaction–diffusion systems

AU - Hausenblas, Erika

AU - Högele, Michael A.

AU - Fahim, Kistosil

PY - 2026

Y1 - 2026

N2 - 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 by linearization systems which have a possibly unbounded, non-dissipative and non-coercive nonlinearity.

AB - 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 by linearization systems which have a possibly unbounded, non-dissipative and non-coercive nonlinearity.

KW - Stochastic Schauder–Tychonoff type theorem

KW - nonlinear stochastic partial differential equation

UR - https://www.scopus.com/pages/publications/105029355619

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DO - 10.1080/17442508.2025.2605337

M3 - Article

AN - SCOPUS:105029355619

SN - 1744-2508

VL - 98

SP - 730

EP - 777

JO - Stochastics

JF - Stochastics

IS - 5

ER -

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

Abstract

Keywords

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