Bifurcation of positive solutions for the one-dimensional (p,q)-Laplace equation
In this article, we study the bifurcation of positive solutions for the one-dimensional (p,q)-Laplace equation under Dirichlet boundary conditions. We investigate the shape of the bifurcation diagram and prove that there exist five different types of bifurcation diagrams. As a consequence, we p...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2017-04-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2017/107/abstr.html |
| _version_ | 1831792095235407872 |
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| author | Ryuji Kajikiya Mieko Tanaka Satoshi Tanaka |
| author_facet | Ryuji Kajikiya Mieko Tanaka Satoshi Tanaka |
| author_sort | Ryuji Kajikiya |
| collection | DOAJ |
| description | In this article, we study the bifurcation of positive solutions for
the one-dimensional (p,q)-Laplace equation under Dirichlet boundary
conditions. We investigate the shape of the bifurcation diagram
and prove that there exist five different types of bifurcation diagrams.
As a consequence, we prove the existence of multiple positive solutions and
show the uniqueness of positive solutions for a bifurcation parameter in
a certain range. |
| first_indexed | 2024-12-22T15:05:13Z |
| format | Article |
| id | doaj.art-c6112e280ce149d5a4ff71e94c1c84ef |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-22T15:05:13Z |
| publishDate | 2017-04-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-c6112e280ce149d5a4ff71e94c1c84ef2022-12-21T18:22:00ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912017-04-012017107,137Bifurcation of positive solutions for the one-dimensional (p,q)-Laplace equationRyuji Kajikiya0Mieko Tanaka1Satoshi Tanaka2 Saga Univ., Saga, Japan Tokyo Univ. of Science, Tokyo, Japan Okayama Univ. of Science, Okayama, Japan In this article, we study the bifurcation of positive solutions for the one-dimensional (p,q)-Laplace equation under Dirichlet boundary conditions. We investigate the shape of the bifurcation diagram and prove that there exist five different types of bifurcation diagrams. As a consequence, we prove the existence of multiple positive solutions and show the uniqueness of positive solutions for a bifurcation parameter in a certain range.http://ejde.math.txstate.edu/Volumes/2017/107/abstr.htmlBifurcationpositive solution(p,q)-Laplace equationtime mapmultiple solutions |
| spellingShingle | Ryuji Kajikiya Mieko Tanaka Satoshi Tanaka Bifurcation of positive solutions for the one-dimensional (p,q)-Laplace equation Electronic Journal of Differential Equations Bifurcation positive solution (p,q)-Laplace equation time map multiple solutions |
| title | Bifurcation of positive solutions for the one-dimensional (p,q)-Laplace equation |
| title_full | Bifurcation of positive solutions for the one-dimensional (p,q)-Laplace equation |
| title_fullStr | Bifurcation of positive solutions for the one-dimensional (p,q)-Laplace equation |
| title_full_unstemmed | Bifurcation of positive solutions for the one-dimensional (p,q)-Laplace equation |
| title_short | Bifurcation of positive solutions for the one-dimensional (p,q)-Laplace equation |
| title_sort | bifurcation of positive solutions for the one dimensional p q laplace equation |
| topic | Bifurcation positive solution (p,q)-Laplace equation time map multiple solutions |
| url | http://ejde.math.txstate.edu/Volumes/2017/107/abstr.html |
| work_keys_str_mv | AT ryujikajikiya bifurcationofpositivesolutionsfortheonedimensionalpqlaplaceequation AT miekotanaka bifurcationofpositivesolutionsfortheonedimensionalpqlaplaceequation AT satoshitanaka bifurcationofpositivesolutionsfortheonedimensionalpqlaplaceequation |