Fractional N-Laplacian Problems Defined on the One-Dimensional Subspace
The research of the fractional Orlicz-Sobolev space and the fractional N-Laplacian operators will give the development of nonlinear elasticity theory, electro rheological fluids, non-Newtonian fluid theory in a porous medium as well as Probability and Analysis as they proved to be accurate models to...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-09-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/13/10/1819 |
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| author | Q-Heung Choi Tacksun Jung |
| author_facet | Q-Heung Choi Tacksun Jung |
| author_sort | Q-Heung Choi |
| collection | DOAJ |
| description | The research of the fractional Orlicz-Sobolev space and the fractional N-Laplacian operators will give the development of nonlinear elasticity theory, electro rheological fluids, non-Newtonian fluid theory in a porous medium as well as Probability and Analysis as they proved to be accurate models to describe different phenomena in Physics, Finance, Image processing and Ecology. We study the number of weak solutions for one-dimensional fractional N-Laplacian systems in the product of the fractional Orlicz-Sobolev spaces, where the corresponding functionals of one-dimensional fractional N-Laplacian systems are even and symmetric. We obtain two results for these problems. One result is that these problems have at least one nontrivial solution under some conditions. The other result is that these problems also have infinitely many weak solutions on the same conditions. We use the variational approach, critical point theory and homology theory on the product of the fractional Orlicz-Sobolev spaces. |
| first_indexed | 2024-03-10T06:10:37Z |
| format | Article |
| id | doaj.art-9c6197f20aa44acd86ee0ee7c3628504 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T06:10:37Z |
| publishDate | 2021-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-9c6197f20aa44acd86ee0ee7c36285042023-11-22T20:09:35ZengMDPI AGSymmetry2073-89942021-09-011310181910.3390/sym13101819Fractional N-Laplacian Problems Defined on the One-Dimensional SubspaceQ-Heung Choi0Tacksun Jung1Department of Mathematics Education, Inha University, Incheon 22212, KoreaDepartment of Mathematics, Kunsan National University, Kunsan 54150, KoreaThe research of the fractional Orlicz-Sobolev space and the fractional N-Laplacian operators will give the development of nonlinear elasticity theory, electro rheological fluids, non-Newtonian fluid theory in a porous medium as well as Probability and Analysis as they proved to be accurate models to describe different phenomena in Physics, Finance, Image processing and Ecology. We study the number of weak solutions for one-dimensional fractional N-Laplacian systems in the product of the fractional Orlicz-Sobolev spaces, where the corresponding functionals of one-dimensional fractional N-Laplacian systems are even and symmetric. We obtain two results for these problems. One result is that these problems have at least one nontrivial solution under some conditions. The other result is that these problems also have infinitely many weak solutions on the same conditions. We use the variational approach, critical point theory and homology theory on the product of the fractional Orlicz-Sobolev spaces.https://www.mdpi.com/2073-8994/13/10/1819fractional N-Laplacian systemsfractional Orlicz-Sobolev spacesproduct of the fractional Orlicz-Sobolev spacesvariational approachcritical point theoryhomology theory |
| spellingShingle | Q-Heung Choi Tacksun Jung Fractional N-Laplacian Problems Defined on the One-Dimensional Subspace Symmetry fractional N-Laplacian systems fractional Orlicz-Sobolev spaces product of the fractional Orlicz-Sobolev spaces variational approach critical point theory homology theory |
| title | Fractional N-Laplacian Problems Defined on the One-Dimensional Subspace |
| title_full | Fractional N-Laplacian Problems Defined on the One-Dimensional Subspace |
| title_fullStr | Fractional N-Laplacian Problems Defined on the One-Dimensional Subspace |
| title_full_unstemmed | Fractional N-Laplacian Problems Defined on the One-Dimensional Subspace |
| title_short | Fractional N-Laplacian Problems Defined on the One-Dimensional Subspace |
| title_sort | fractional n laplacian problems defined on the one dimensional subspace |
| topic | fractional N-Laplacian systems fractional Orlicz-Sobolev spaces product of the fractional Orlicz-Sobolev spaces variational approach critical point theory homology theory |
| url | https://www.mdpi.com/2073-8994/13/10/1819 |
| work_keys_str_mv | AT qheungchoi fractionalnlaplacianproblemsdefinedontheonedimensionalsubspace AT tacksunjung fractionalnlaplacianproblemsdefinedontheonedimensionalsubspace |