An order approach to SPDEs with antimonotone terms

TL;DR

This paper develops an order-based method to establish the existence of unique extremal solutions for a class of parabolic SPDEs with antimonotone nonlinearities, using fixed-point and comparison principles.

Contribution

It introduces a novel order approach for proving existence and uniqueness of solutions to SPDEs with antimonotone terms, expanding the theoretical framework.

Findings

Existence of unique maximal and minimal solutions established.

Comparison principle validated for the class of SPDEs considered.

Fixed-point argument successfully applied in ordered spaces.

Abstract

We consider a class of parabolic stochastic partial differential equations featuring an antimonotone nonlinearity. The existence of unique maximal and minimal variational solutions is proved via a fixed-point argument for nondecreasing mappings in ordered spaces. This relies on the validity of a comparison principle.