Multiplicity of positive solutions to a singular $(p_1,p_2)$-Laplacian system with coupled integral boundary conditions
In this work, we investigate the existence and multiplicity results for positive solutions to a singular $(p_1,p_2)$-Laplacian system with coupled integral boundary conditions and a parameter $(\mu,\lambda) \in \mathbb{R}_+^3 $. Using sub-super solutions method and fixed point index theorems, it is...
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| Format: | Article |
| Language: | English |
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University of Szeged
2016-06-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Subjects: | |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=4229 |
| _version_ | 1797830570229628928 |
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| author | Jeongmi Jeong Chan-Gyun Kim EUN KYOUNG LEE |
| author_facet | Jeongmi Jeong Chan-Gyun Kim EUN KYOUNG LEE |
| author_sort | Jeongmi Jeong |
| collection | DOAJ |
| description | In this work, we investigate the existence and multiplicity results for positive solutions to a singular $(p_1,p_2)$-Laplacian system with coupled integral boundary conditions and a parameter $(\mu,\lambda) \in \mathbb{R}_+^3 $. Using sub-super solutions method and fixed point index theorems, it is shown that there exists a continuous surface $\mathcal{C}$ which separates $\mathbb{R}_+^2 \times (0,\infty)$ into two regions $\mathcal{O}_1$ and $\mathcal{O}_2$ such that the problem under consideration has two positive solutions for $( \mu,\lambda) \in \mathcal{O}_1,$ at least one positive solution for $( \mu,\lambda) \in \mathcal{C}$, and no positive solutions for $( \mu,\lambda) \in \mathcal{O}_2.$ |
| first_indexed | 2024-04-09T13:39:17Z |
| format | Article |
| id | doaj.art-465d241a121e496ab34e0c0a6300af3f |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:39:17Z |
| publishDate | 2016-06-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-465d241a121e496ab34e0c0a6300af3f2023-05-09T07:53:05ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752016-06-0120163212310.14232/ejqtde.2016.1.324229Multiplicity of positive solutions to a singular $(p_1,p_2)$-Laplacian system with coupled integral boundary conditionsJeongmi Jeong0Chan-Gyun Kim1EUN KYOUNG LEE2Department of Mathematics, Pusan National University, Busan, KoreaDepartment of Mathematics Education, Pusan National University, Busan, KoreaDepartment of Mathematics Education, Pusan National University, Jangjeon-dong, Geumjeong-gu, Busan, KoreaIn this work, we investigate the existence and multiplicity results for positive solutions to a singular $(p_1,p_2)$-Laplacian system with coupled integral boundary conditions and a parameter $(\mu,\lambda) \in \mathbb{R}_+^3 $. Using sub-super solutions method and fixed point index theorems, it is shown that there exists a continuous surface $\mathcal{C}$ which separates $\mathbb{R}_+^2 \times (0,\infty)$ into two regions $\mathcal{O}_1$ and $\mathcal{O}_2$ such that the problem under consideration has two positive solutions for $( \mu,\lambda) \in \mathcal{O}_1,$ at least one positive solution for $( \mu,\lambda) \in \mathcal{C}$, and no positive solutions for $( \mu,\lambda) \in \mathcal{O}_2.$http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=4229nonlocal boundary conditionmultiplicitypositive solutionsingular weight function |
| spellingShingle | Jeongmi Jeong Chan-Gyun Kim EUN KYOUNG LEE Multiplicity of positive solutions to a singular $(p_1,p_2)$-Laplacian system with coupled integral boundary conditions Electronic Journal of Qualitative Theory of Differential Equations nonlocal boundary condition multiplicity positive solution singular weight function |
| title | Multiplicity of positive solutions to a singular $(p_1,p_2)$-Laplacian system with coupled integral boundary conditions |
| title_full | Multiplicity of positive solutions to a singular $(p_1,p_2)$-Laplacian system with coupled integral boundary conditions |
| title_fullStr | Multiplicity of positive solutions to a singular $(p_1,p_2)$-Laplacian system with coupled integral boundary conditions |
| title_full_unstemmed | Multiplicity of positive solutions to a singular $(p_1,p_2)$-Laplacian system with coupled integral boundary conditions |
| title_short | Multiplicity of positive solutions to a singular $(p_1,p_2)$-Laplacian system with coupled integral boundary conditions |
| title_sort | multiplicity of positive solutions to a singular p 1 p 2 laplacian system with coupled integral boundary conditions |
| topic | nonlocal boundary condition multiplicity positive solution singular weight function |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=4229 |
| work_keys_str_mv | AT jeongmijeong multiplicityofpositivesolutionstoasingularp1p2laplaciansystemwithcoupledintegralboundaryconditions AT changyunkim multiplicityofpositivesolutionstoasingularp1p2laplaciansystemwithcoupledintegralboundaryconditions AT eunkyounglee multiplicityofpositivesolutionstoasingularp1p2laplaciansystemwithcoupledintegralboundaryconditions |