Critical points of a class of functionals in a Sobolev space

Shokooh, Saeid; Alizadeh Afrouzi, Ghasem

doi:10.22055/jamm.2025.49192.2355

Critical points of a class of functionals in a Sobolev space

Document Type : Original Paper

Authors

Saeid Shokooh ¹

Ghasem Alizadeh Afrouzi ²

¹ Department of Mathematics, Faculty of Sciences, Gonbad Kavous University,Gonbad Kavous

² Department of Mathematics, Faculty of Matheatics Sciences, University of Mazandaran, Babolsar, Iran

10.22055/jamm.2025.49192.2355

Abstract

In this paper, we investigate the existence of critical points for a specific class of functionals using critical point theorems. These critical points are of particular importance because they are associated with weak solutions to integral-differential problems with Dirichlet boundary conditions. Indeed, by employing variational methods, we first study the existence of a critical point for a functional with one control parameter and then examine the existence of a sequence of critical points for a functional with two parameters.

Highlights

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Keywords

Integro-differential equations

critical points

weak solution

Subjects