Minimizing a class of polyconvex functionals involving Caputo derivatives
In this article, we establish the existence of multiple, infinitely many, nontrivial solutions to a class of nonlinear fractional elliptic systems in fractional variational form subject to pointwise gradient constraint and pure Dirichlet-type boundary conditions. We use a topological class of maps r...
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| Published in | Boundary value problems Vol. 2024; no. 1; pp. 118 - 22 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
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27.09.2024
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| Abstract | In this article, we establish the existence of multiple,
infinitely
many, nontrivial solutions to a class of nonlinear fractional elliptic systems in fractional variational form subject to pointwise gradient constraint and pure Dirichlet-type boundary conditions. We use a topological class of maps referred to as
generalized
twists and examine them in connection with the later system of fractional Euler-Lagrange equations and prove the existence of a countably infinite of topologically distinct twisting solutions to this system. |
|---|---|
| AbstractList | Abstract In this article, we establish the existence of multiple, infinitely many, nontrivial solutions to a class of nonlinear fractional elliptic systems in fractional variational form subject to pointwise gradient constraint and pure Dirichlet-type boundary conditions. We use a topological class of maps referred to as generalized twists and examine them in connection with the later system of fractional Euler-Lagrange equations and prove the existence of a countably infinite of topologically distinct twisting solutions to this system. In this article, we establish the existence of multiple, infinitely many, nontrivial solutions to a class of nonlinear fractional elliptic systems in fractional variational form subject to pointwise gradient constraint and pure Dirichlet-type boundary conditions. We use a topological class of maps referred to as generalized twists and examine them in connection with the later system of fractional Euler-Lagrange equations and prove the existence of a countably infinite of topologically distinct twisting solutions to this system. In this article, we establish the existence of multiple, infinitely many, nontrivial solutions to a class of nonlinear fractional elliptic systems in fractional variational form subject to pointwise gradient constraint and pure Dirichlet-type boundary conditions. We use a topological class of maps referred to as generalized twists and examine them in connection with the later system of fractional Euler-Lagrange equations and prove the existence of a countably infinite of topologically distinct twisting solutions to this system. |
| ArticleNumber | 118 |
| Author | Shahrokhi-Dehkordi, M. S. Toosnezhad, F. |
| Author_xml | – sequence: 1 givenname: F. surname: Toosnezhad fullname: Toosnezhad, F. organization: Department of Applied Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University – sequence: 2 givenname: M. S. surname: Shahrokhi-Dehkordi fullname: Shahrokhi-Dehkordi, M. S. email: Shahrokhi@ipm.ir organization: Department of Applied Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University |
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| Cites_doi | 10.1007/s00526-008-0202-5 10.1515/acv-2016-0056 10.1155/2013/605412 10.1142/p871 10.1007/s43037-020-00097-4 10.3390/fractalfract7020137 10.1007/978-3-319-14756-7 10.1007/978-0-387-98128-4 10.1016/j.anihpc.2020.02.006 10.1016/j.jmaa.2012.10.008 10.1016/S0304-0208(06)80001-0 10.1007/0-387-21791-6_1 10.1515/fca-2016-0029 10.1007/978-3-540-69952-1 10.1103/PhysRevE.55.3581 10.12775/TMNA.2009.013 10.1016/j.aop.2008.04.005 10.1515/acv-2014-0009 10.1016/j.cnsns.2010.07.016 10.1016/j.physleta.2011.08.033 10.1515/ACV.2009.014 10.1007/978-3-642-14574-2 10.1103/PhysRevE.53.1890 10.1142/8072 10.18576/pfda/080404 10.1007/s11118-018-9684-8 10.1007/978-1-4613-8165-5 10.1007/978-1-4757-6848-0 |
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A – volume: 53 start-page: 1890 issue: 3 year: 1996 ident: 1927_CR24 publication-title: Phys. Rev. E doi: 10.1103/PhysRevE.53.1890 – volume: 50 start-page: 327 issue: 3 year: 2019 ident: 1927_CR29 publication-title: Potential Anal. doi: 10.1007/s11118-018-9684-8 – volume-title: Introduction to the Fractional Calculus of Variations year: 2012 ident: 1927_CR38 – volume-title: Optimization—Theory and Applications: Problems with Ordinary Differential Equations year: 1983 ident: 1927_CR10 doi: 10.1007/978-1-4613-8165-5 – volume: 20 start-page: 213 year: 2015 ident: 1927_CR8 publication-title: Adv. Differ. Equ. – volume: 8 start-page: 321 issue: 4 year: 2015 ident: 1927_CR32 publication-title: Adv. Calc. Var. doi: 10.1515/acv-2014-0009 – volume: 33 start-page: 179 issue: 1 year: 2009 ident: 1927_CR35 publication-title: Topol. Methods Nonlinear Anal. doi: 10.12775/TMNA.2009.013 – volume: 7 start-page: 137 issue: 2 year: 2023 ident: 1927_CR37 publication-title: Fractal Fract. doi: 10.3390/fractalfract7020137 – start-page: 3 volume-title: Geometry, Mechanics and Dynamics year: 2002 ident: 1927_CR4 doi: 10.1007/0-387-21791-6_1 – volume-title: Fractional Differential Equations year: 1999 ident: 1927_CR23 – volume: 5 start-page: 1 issue: 4 year: 2019 ident: 1927_CR26 publication-title: Prog. Fract. Differ. Appl. – volume: 11 start-page: 289 issue: 3 year: 2018 ident: 1927_CR33 publication-title: Adv. Calc. Var. doi: 10.1515/acv-2016-0056 – volume: 399 start-page: 239 year: 2013 ident: 1927_CR7 publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2012.10.008 – volume-title: The Analysis of Fractional Differential Equations: An Application Oriented Exposition Using Differential Operators of Caputo Type year: 2010 ident: 1927_CR12 doi: 10.1007/978-3-642-14574-2 – volume: 55 start-page: 3581 issue: 3 year: 1997 ident: 1927_CR25 publication-title: Phys. Rev. E doi: 10.1103/PhysRevE.55.3581 – volume: 8 start-page: 495 issue: 4 year: 2022 ident: 1927_CR27 publication-title: Prog. Fract. Differ. Appl. doi: 10.18576/pfda/080404 – volume-title: Fractional Integral and Derivative, Theory and Applications year: 1993 ident: 1927_CR28 – volume-title: Direct Methods in the Calculus of Variations year: 2007 ident: 1927_CR11 – volume: 19 start-page: 561 year: 2016 ident: 1927_CR13 publication-title: Fract. Calc. Appl. Anal. doi: 10.1515/fca-2016-0029 – volume-title: Fractional Differentiation Inequalities year: 2009 ident: 1927_CR2 doi: 10.1007/978-0-387-98128-4 – volume-title: Introduction to the Fractional Calculus of Variations year: 2012 ident: 1927_CR20 doi: 10.1142/p871 – volume: 35 start-page: 191 issue: 2 year: 2009 ident: 1927_CR31 publication-title: Calc. Var. Partial Differ. Equ. doi: 10.1007/s00526-008-0202-5 – volume: 2013 year: 2013 ident: 1927_CR39 publication-title: Sci. World J. doi: 10.1155/2013/605412 – volume: 323 start-page: 137 year: 2008 ident: 1927_CR36 publication-title: Ann. Phys. doi: 10.1016/j.aop.2008.04.005 – volume-title: Multiple Integrals in the Calculus of Variations year: 1966 ident: 1927_CR21 doi: 10.1007/978-3-540-69952-1 – volume: 15 year: 2021 ident: 1927_CR15 publication-title: Banach J. Math. Anal. doi: 10.1007/s43037-020-00097-4 – volume-title: The Fractional Calculus year: 1974 ident: 1927_CR22 – volume-title: Advanced Methods in the Fractional Calculus of Variations year: 2015 ident: 1927_CR19 doi: 10.1007/978-3-319-14756-7 |
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| Snippet | In this article, we establish the existence of multiple,
infinitely
many, nontrivial solutions to a class of nonlinear fractional elliptic systems in... In this article, we establish the existence of multiple, infinitely many, nontrivial solutions to a class of nonlinear fractional elliptic systems in... Abstract In this article, we establish the existence of multiple, infinitely many, nontrivial solutions to a class of nonlinear fractional elliptic systems in... |
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| SubjectTerms | Analysis Applied mathematics Approximations and Expansions Boundary conditions Boundary value problems Calculus Difference and Functional Equations Elliptic functions Euler-Lagrange equation Fractional calculus Mathematics Mathematics and Statistics Natural boundary conditions Nonlinear systems Ordinary Differential Equations Partial Differential Equations Polyconvexity Twist maps |
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| Title | Minimizing a class of polyconvex functionals involving Caputo derivatives |
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