Solutions to nonlocal evolution equations governed by non-autonomous forms and demicontinuous nonlinearities

TL;DR

This paper establishes the existence of solutions with L2 regularity for non-autonomous evolution equations involving nonlocal conditions, using a combination of finite-dimensional reduction and Leray-Schauder methods.

Contribution

It introduces a novel approach that combines finite-dimensional reduction with Leray-Schauder continuation to handle a broad class of nonlinearities with demicontinuity.

Findings

Existence of L2 regular solutions for non-autonomous evolution equations.

Applicable to equations with nonlocal conditions and demicontinuous nonlinearities.

Method broadens the scope of solvable nonlinear evolution equations.

Abstract

We deal with the existence of solutions having L2 regularity for a class of non autonomous evolution equations. Associated with the equation, a general non local condition is studied. The technique we used combines a finite dimensional reduction together with the Leray-Schauder continuation principle. This approach permits to consider a wide class of nonlinear terms by allowing demicontinuity assumptions on the nonlinearity.