Positive solutions for eigenvalue problems of fractional q-difference equation with ϕ-Laplacian
Abstract The aim of this paper is to investigate the boundary value problem of a fractional q-difference equation with ϕ-Laplacian, where ϕ-Laplacian is a generalized p-Laplacian operator. We obtain the existence and nonexistence of positive solutions in terms of different eigenvalue intervals for t...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2021-11-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13662-021-03652-x |
| _version_ | 1818344539265433600 |
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| author | Jufang Wang Changlong Yu Boya Zhang Si Wang |
| author_facet | Jufang Wang Changlong Yu Boya Zhang Si Wang |
| author_sort | Jufang Wang |
| collection | DOAJ |
| description | Abstract The aim of this paper is to investigate the boundary value problem of a fractional q-difference equation with ϕ-Laplacian, where ϕ-Laplacian is a generalized p-Laplacian operator. We obtain the existence and nonexistence of positive solutions in terms of different eigenvalue intervals for this problem by means of the Green function and Guo–Krasnoselskii fixed point theorem on cones. Finally, we give some examples to illustrate the use of our results. |
| first_indexed | 2024-12-13T16:48:05Z |
| format | Article |
| id | doaj.art-e523161cc28c4dda9ce6ba633d797889 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-13T16:48:05Z |
| publishDate | 2021-11-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-e523161cc28c4dda9ce6ba633d7978892022-12-21T23:38:07ZengSpringerOpenAdvances in Difference Equations1687-18472021-11-012021111510.1186/s13662-021-03652-xPositive solutions for eigenvalue problems of fractional q-difference equation with ϕ-LaplacianJufang Wang0Changlong Yu1Boya Zhang2Si Wang3College of Sciences, Hebei University of Science and TechnologyCollege of Sciences, Hebei University of Science and TechnologyCollege of Sciences, Hebei University of Science and TechnologyCollege of Sciences, Hebei University of Science and TechnologyAbstract The aim of this paper is to investigate the boundary value problem of a fractional q-difference equation with ϕ-Laplacian, where ϕ-Laplacian is a generalized p-Laplacian operator. We obtain the existence and nonexistence of positive solutions in terms of different eigenvalue intervals for this problem by means of the Green function and Guo–Krasnoselskii fixed point theorem on cones. Finally, we give some examples to illustrate the use of our results.https://doi.org/10.1186/s13662-021-03652-xFractional q-difference equationsPositive solutionsBoundary value problemGuo–Krasnoselskii fixed point theorem |
| spellingShingle | Jufang Wang Changlong Yu Boya Zhang Si Wang Positive solutions for eigenvalue problems of fractional q-difference equation with ϕ-Laplacian Advances in Difference Equations Fractional q-difference equations Positive solutions Boundary value problem Guo–Krasnoselskii fixed point theorem |
| title | Positive solutions for eigenvalue problems of fractional q-difference equation with ϕ-Laplacian |
| title_full | Positive solutions for eigenvalue problems of fractional q-difference equation with ϕ-Laplacian |
| title_fullStr | Positive solutions for eigenvalue problems of fractional q-difference equation with ϕ-Laplacian |
| title_full_unstemmed | Positive solutions for eigenvalue problems of fractional q-difference equation with ϕ-Laplacian |
| title_short | Positive solutions for eigenvalue problems of fractional q-difference equation with ϕ-Laplacian |
| title_sort | positive solutions for eigenvalue problems of fractional q difference equation with ϕ laplacian |
| topic | Fractional q-difference equations Positive solutions Boundary value problem Guo–Krasnoselskii fixed point theorem |
| url | https://doi.org/10.1186/s13662-021-03652-x |
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