Evolution Differential Equations in Fr\'echet Space with Schauder Basis

TL;DR

This paper develops a method for solving evolution differential equations in Fréchet spaces with Schauder bases, providing existence theorems for Cauchy problems and applications to PDEs and ODEs.

Contribution

It introduces a novel majorant functions method tailored for Fréchet spaces with Schauder bases, enabling new existence results for evolution equations.

Findings

Established existence theorems for Cauchy problems in Fréchet spaces.

Applied the method to specific PDE and ODE problems.

Extended classical techniques to a broader functional analytic setting.

Abstract

We consider evolution differential equations in Fr\'echet spaces that possess unconditional Schauder basis and construct a version of the majorant functions method to obtain existence theorems for Cauchy problems. Applications to PDE and ODE have been considered.