# Recursive Variational Problems in Nonreflexive Banach Spaces with an Infinite Horizon: An Existence Result

## TL;DR

This paper establishes the existence of solutions for recursive variational problems with infinite horizons in nonreflexive Banach spaces, expanding the theoretical understanding of such problems in infinite-dimensional settings.

## Contribution

It provides an existence theorem for solutions to recursive variational problems with infinite horizons in nonreflexive Banach spaces, using Cesari type conditions.

## Key findings

- Existence of optimal solutions in Sobolev spaces for the problem.
- Conditions ensuring solutions to the initial value problem.
- Extension of variational problem theory to nonreflexive Banach spaces.

## Abstract

We investigate variational problems with recursive integral functionals governed by infinite-dimensional differential inclusions with an infinite horizon and present an existence result in the setting of nonreflexive Banach spaces. We find an optimal solution in a Sobolev space taking values in a Banach space under the Cesari type condition. We also investigate sufficient conditions for the existence of solutions to the initial value problem for the differential inclusion.