On Local Weak Solutions for Fractional in Time SOBOLEV-Type Inequalities

On Local Weak Solutions for Fractional in Time SOBOLEV-Type Inequalities

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 cr...

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Main Authors: Mohaemd Jleli, Bessem Samet
Format: Article
Language:English
Published: Hindawi Limited 2020-01-01
Series:Journal of Function Spaces
Online Access:http://dx.doi.org/10.1155/2020/4867186
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spelling doaj-27b72184522a4b30b3cc683da81545742020-11-25T03:53:41ZengHindawi LimitedJournal of Function Spaces2314-88962314-88882020-01-01202010.1155/2020/48671864867186On Local Weak Solutions for Fractional in Time SOBOLEV-Type InequalitiesMohaemd Jleli0Bessem Samet1Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi ArabiaDepartment of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi ArabiaWe 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.http://dx.doi.org/10.1155/2020/4867186
collection DOAJ
language English
format Article
sources DOAJ
author Mohaemd Jleli
Bessem Samet
spellingShingle Mohaemd Jleli
Bessem Samet
On Local Weak Solutions for Fractional in Time SOBOLEV-Type Inequalities
Journal of Function Spaces
author_facet Mohaemd Jleli
Bessem Samet
author_sort Mohaemd Jleli
title On Local Weak Solutions for Fractional in Time SOBOLEV-Type Inequalities
title_short On Local Weak Solutions for Fractional in Time SOBOLEV-Type Inequalities
title_full On Local Weak Solutions for Fractional in Time SOBOLEV-Type Inequalities
title_fullStr On Local Weak Solutions for Fractional in Time SOBOLEV-Type Inequalities
title_full_unstemmed On Local Weak Solutions for Fractional in Time SOBOLEV-Type Inequalities
title_sort on local weak solutions for fractional in time sobolev-type inequalities
publisher Hindawi Limited
series Journal of Function Spaces
issn 2314-8896
2314-8888
publishDate 2020-01-01
description 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.
url http://dx.doi.org/10.1155/2020/4867186
work_keys_str_mv AT mohaemdjleli onlocalweaksolutionsforfractionalintimesobolevtypeinequalities
AT bessemsamet onlocalweaksolutionsforfractionalintimesobolevtypeinequalities
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