Existence of three solutions for a class of fractional boundary value systems

Mohseni Kolagar, Samad; Afrouzi, Ghasem A.; Hadjian, Armin

doi:10.22075/ijnaa.2017.1241.1296

Existence of three solutions for a class of fractional boundary value systems

Document Type : Research Paper

Authors

Samad Mohseni Kolagar ¹

Ghasem A. Afrouzi ¹

Armin Hadjian ²

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

² Department of Mathematics, Faculty of Basic Sciences, University of Bojnord, P.O. Box 1339, Bojnord 94531, Iran

10.22075/ijnaa.2017.1241.1296

Abstract

In this paper, under appropriate oscillating behaviours of the nonlinear term, we prove some multiplicity results for a class of nonlinear fractional equations. These problems have a variational structure and we find three solutions for them by exploiting an abstract result for smooth functionals defined on a reflexive Banach space. To make the nonlinear methods work, some careful analysis of the fractional spaces involved is necessary. We also give an example to illustrate the obtained result.

Keywords

Fractional differential equations

Riemann-Liouville fractional derivatives

Variational methods

Three solutions