On Local Weak Solutions for Fractional in Time SOBOLEV-Type Inequalities. (23rd September 2020)

• Record Type: Journal Article
• Authors: Jleli, Mohaemd; Samet, Bessem
• Other Names: Mitrovic Zoran Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2020(2020)
• Publication Date: 2020-09-23
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2020/4867186
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : We consider two fractional in time nonlinear Sobolev-type inequalities involving potential terms, where the fractional derivatives are defined in the sense of Caputo. For both problems, we study the existence and nonexistence of nontrivial local weak solutions. Namely, we show that there exists a critical exponent according to which we have existence or nonexistence.