Global structure of positive solutions for third-order semipositone integral boundary value problems
<p>In this paper, we were concerned with the global behavior of positive solutions for third-order semipositone problems with an integral boundary condition</p> <p class="disp_formula">$ \begin{equation*} \begin{split} &y'''+\beta y''+\...
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| Format: | Article |
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AIMS Press
2024-02-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2024353?viewType=HTML |
| _version_ | 1827338202626654208 |
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| author | Zhonghua Bi Sanyang Liu |
| author_facet | Zhonghua Bi Sanyang Liu |
| author_sort | Zhonghua Bi |
| collection | DOAJ |
| description | <p>In this paper, we were concerned with the global behavior of positive solutions for third-order semipositone problems with an integral boundary condition</p>
<p class="disp_formula">$ \begin{equation*} \begin{split} &y'''+\beta y''+\alpha y'+\lambda f(t,y) = 0,\; \; \; t\in(0,1),\\ &y(0) = y'(0) = 0,\; \; \; y(1) = \chi\int^1_0y(s)ds, \end{split} \end{equation*} $</p>
<p>where $ \alpha\in(0, \infty) $ and $ \beta\in(-\infty, \infty) $ are two constants, $ \lambda, \chi $ are two positive parameters, and $ f\in C([0, 1]\times[0, \infty), \mathbb{R}) $ with $ f(t, 0) < 0 $. Our analysis mainly relied on the bifurcation theory.</p> |
| first_indexed | 2024-03-07T19:11:19Z |
| format | Article |
| id | doaj.art-6e0409eb243f45378525bbffd6a18729 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-07T19:11:19Z |
| publishDate | 2024-02-01 |
| publisher | AIMS Press |
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| series | AIMS Mathematics |
| spelling | doaj.art-6e0409eb243f45378525bbffd6a187292024-03-01T01:13:45ZengAIMS PressAIMS Mathematics2473-69882024-02-01937273729210.3934/math.2024353Global structure of positive solutions for third-order semipositone integral boundary value problemsZhonghua Bi0Sanyang Liu1School of Mathematics and Statistics, Xidian University, Xi'an, 710126, ChinaSchool of Mathematics and Statistics, Xidian University, Xi'an, 710126, China<p>In this paper, we were concerned with the global behavior of positive solutions for third-order semipositone problems with an integral boundary condition</p> <p class="disp_formula">$ \begin{equation*} \begin{split} &y'''+\beta y''+\alpha y'+\lambda f(t,y) = 0,\; \; \; t\in(0,1),\\ &y(0) = y'(0) = 0,\; \; \; y(1) = \chi\int^1_0y(s)ds, \end{split} \end{equation*} $</p> <p>where $ \alpha\in(0, \infty) $ and $ \beta\in(-\infty, \infty) $ are two constants, $ \lambda, \chi $ are two positive parameters, and $ f\in C([0, 1]\times[0, \infty), \mathbb{R}) $ with $ f(t, 0) < 0 $. Our analysis mainly relied on the bifurcation theory.</p>https://www.aimspress.com/article/doi/10.3934/math.2024353?viewType=HTMLpositive solutionssemipositonethird-order integral boundary value problemsbifurcation |
| spellingShingle | Zhonghua Bi Sanyang Liu Global structure of positive solutions for third-order semipositone integral boundary value problems AIMS Mathematics positive solutions semipositone third-order integral boundary value problems bifurcation |
| title | Global structure of positive solutions for third-order semipositone integral boundary value problems |
| title_full | Global structure of positive solutions for third-order semipositone integral boundary value problems |
| title_fullStr | Global structure of positive solutions for third-order semipositone integral boundary value problems |
| title_full_unstemmed | Global structure of positive solutions for third-order semipositone integral boundary value problems |
| title_short | Global structure of positive solutions for third-order semipositone integral boundary value problems |
| title_sort | global structure of positive solutions for third order semipositone integral boundary value problems |
| topic | positive solutions semipositone third-order integral boundary value problems bifurcation |
| url | https://www.aimspress.com/article/doi/10.3934/math.2024353?viewType=HTML |
| work_keys_str_mv | AT zhonghuabi globalstructureofpositivesolutionsforthirdordersemipositoneintegralboundaryvalueproblems AT sanyangliu globalstructureofpositivesolutionsforthirdordersemipositoneintegralboundaryvalueproblems |