Note on the existence theory for evolution equations with pseudo-monotone operators

TL;DR

This paper introduces a framework for establishing the existence of solutions to evolution equations involving pseudo-monotone operators, simplifying verification in practical applications.

Contribution

It provides an abstract existence theorem for evolution equations with pseudo-monotone operators, applicable to various concrete problems.

Findings

Framework simplifies proving existence of solutions.

Assumptions are easily verifiable in real-world examples.

Applicable to a broad class of evolution equations.

Abstract

In this note we present a framework which allows to prove an abstract existence result for evolution equations with pseudo-monotone operators. The assumptions on the spaces and the operators can be easily verified in concrete examples.