Global behavior of positive solutions for some semipositone fourth-order problems
Abstract In this paper, we study the global behavior of positive solutions of fourth-order boundary value problems {u′′′′=λf(x,u),x∈(0,1),u(0)=u(1)=u″(0)=u″(1)=0, $$ \textstyle\begin{cases} u''''=\lambda f(x,u), \quad x\in (0,1), \\ u(0)=u(1)=u''(0)=u''(1)=0,...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2018-12-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-018-1904-4 |
| _version_ | 1817998583747575808 |
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| author | Dongliang Yan Ruyun Ma |
| author_facet | Dongliang Yan Ruyun Ma |
| author_sort | Dongliang Yan |
| collection | DOAJ |
| description | Abstract In this paper, we study the global behavior of positive solutions of fourth-order boundary value problems {u′′′′=λf(x,u),x∈(0,1),u(0)=u(1)=u″(0)=u″(1)=0, $$ \textstyle\begin{cases} u''''=\lambda f(x,u), \quad x\in (0,1), \\ u(0)=u(1)=u''(0)=u''(1)=0, \end{cases} $$ where f:[0,1]×R+→R $f: [0,1]\times \mathbb{R^{+}} \to \mathbb{R}$ is a continuous function with f(x,0)<0 $f(x,0)<0$ in (0,1) $(0, 1)$, and λ>0 $\lambda >0$. The proof of our main results are based upon bifurcation techniques. |
| first_indexed | 2024-04-14T02:55:29Z |
| format | Article |
| id | doaj.art-31ac3c94480d42bba87c462c8afdb5c7 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-04-14T02:55:29Z |
| publishDate | 2018-12-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-31ac3c94480d42bba87c462c8afdb5c72022-12-22T02:16:07ZengSpringerOpenAdvances in Difference Equations1687-18472018-12-012018111410.1186/s13662-018-1904-4Global behavior of positive solutions for some semipositone fourth-order problemsDongliang Yan0Ruyun Ma1Department of Mathematics, Northwest Normal UniversityDepartment of Mathematics, Northwest Normal UniversityAbstract In this paper, we study the global behavior of positive solutions of fourth-order boundary value problems {u′′′′=λf(x,u),x∈(0,1),u(0)=u(1)=u″(0)=u″(1)=0, $$ \textstyle\begin{cases} u''''=\lambda f(x,u), \quad x\in (0,1), \\ u(0)=u(1)=u''(0)=u''(1)=0, \end{cases} $$ where f:[0,1]×R+→R $f: [0,1]\times \mathbb{R^{+}} \to \mathbb{R}$ is a continuous function with f(x,0)<0 $f(x,0)<0$ in (0,1) $(0, 1)$, and λ>0 $\lambda >0$. The proof of our main results are based upon bifurcation techniques.http://link.springer.com/article/10.1186/s13662-018-1904-434B1834B1634B2547H11 |
| spellingShingle | Dongliang Yan Ruyun Ma Global behavior of positive solutions for some semipositone fourth-order problems Advances in Difference Equations 34B18 34B16 34B25 47H11 |
| title | Global behavior of positive solutions for some semipositone fourth-order problems |
| title_full | Global behavior of positive solutions for some semipositone fourth-order problems |
| title_fullStr | Global behavior of positive solutions for some semipositone fourth-order problems |
| title_full_unstemmed | Global behavior of positive solutions for some semipositone fourth-order problems |
| title_short | Global behavior of positive solutions for some semipositone fourth-order problems |
| title_sort | global behavior of positive solutions for some semipositone fourth order problems |
| topic | 34B18 34B16 34B25 47H11 |
| url | http://link.springer.com/article/10.1186/s13662-018-1904-4 |
| work_keys_str_mv | AT dongliangyan globalbehaviorofpositivesolutionsforsomesemipositonefourthorderproblems AT ruyunma globalbehaviorofpositivesolutionsforsomesemipositonefourthorderproblems |