Mountain pass solutions for nonlocal fractional elliptic operators

Hamidi, Nadere; Afrouzi, Ghasem; Mirzapour, Maryam

doi:10.22075/ijnaa.2026.39729.5577

Mountain pass solutions for nonlocal fractional elliptic operators

Articles in Press

Document Type : Research Paper

Authors

Nadere Hamidi ¹

Ghasem Afrouzi ¹

Maryam Mirzapour ²

¹ Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran

² Department of Mathematics Education, Farhangian University, P.O. Box 14665-889, Tehran, Iran

10.22075/ijnaa.2026.39729.5577

Abstract

The purpose of this paper is to check the existence of solutions to nonlocal integrodifferential operators. These equations have a nontrivial variational structure solution using the Mountain Pass Theorem. To effectively employ the nonlinear methodologies, a comprehensive and rigorous analysis of the fractional spaces involved is imperative. In addition, we require rather general assumptions on the local operator.

Keywords

Variational techniques

Mountain Pass Theorem

Integrodiﬀerential operators

Fractional Laplacian

Nonlocal problems

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