Shooting method in the application of boundary value problems for differential equations with sign-changing weight function
In this paper, we use the shooting method to study the solvability of the boundary value problem of differential equations with sign-changing weight function: u″(t)+(λa+(t)−μa−(t))g(u)=0,0<t<T,u′(0)=0,u′(T)=0,\left\{\phantom{\rule[-1.25em]{}{0ex}}\begin{array}{l}{u}^{^{\prime\prime} }\left(t)+...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2022-08-01
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| Series: | Open Mathematics |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/math-2022-0062 |
| _version_ | 1797998369568718848 |
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| author | Yue Xu Xiaoling Han |
| author_facet | Yue Xu Xiaoling Han |
| author_sort | Yue Xu |
| collection | DOAJ |
| description | In this paper, we use the shooting method to study the solvability of the boundary value problem of differential equations with sign-changing weight function: u″(t)+(λa+(t)−μa−(t))g(u)=0,0<t<T,u′(0)=0,u′(T)=0,\left\{\phantom{\rule[-1.25em]{}{0ex}}\begin{array}{l}{u}^{^{\prime\prime} }\left(t)+\left(\lambda {a}^{+}\left(t)-\mu {a}^{-}\left(t))g\left(u)=0,\hspace{1.0em}0\lt t\lt T,\\ u^{\prime} \left(0)=0,\hspace{1.0em}u^{\prime} \left(T)=0,\end{array}\right. where a∈L[0,T]a\in L\left[0,T] is sign-changing and the nonlinearity g:[0,∞)→Rg:{[}0,\infty )\to {\mathbb{R}} is continuous such that g(0)=g(1)=g(2)=0g\left(0)=g\left(1)=g\left(2)=0, g(s)>0g\left(s)\gt 0 for s∈(0,1)s\in \left(0,1), g(s)<0g\left(s)\lt 0 for s∈(1,2)s\in \left(1,2). |
| first_indexed | 2024-04-11T10:47:37Z |
| format | Article |
| id | doaj.art-648b7cb6133a4a40a8433ac000feb7b1 |
| institution | Directory Open Access Journal |
| issn | 2391-5455 |
| language | English |
| last_indexed | 2024-04-11T10:47:37Z |
| publishDate | 2022-08-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj.art-648b7cb6133a4a40a8433ac000feb7b12022-12-22T04:29:00ZengDe GruyterOpen Mathematics2391-54552022-08-0120174375010.1515/math-2022-0062Shooting method in the application of boundary value problems for differential equations with sign-changing weight functionYue Xu0Xiaoling Han1College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, ChinaCollege of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, ChinaIn this paper, we use the shooting method to study the solvability of the boundary value problem of differential equations with sign-changing weight function: u″(t)+(λa+(t)−μa−(t))g(u)=0,0<t<T,u′(0)=0,u′(T)=0,\left\{\phantom{\rule[-1.25em]{}{0ex}}\begin{array}{l}{u}^{^{\prime\prime} }\left(t)+\left(\lambda {a}^{+}\left(t)-\mu {a}^{-}\left(t))g\left(u)=0,\hspace{1.0em}0\lt t\lt T,\\ u^{\prime} \left(0)=0,\hspace{1.0em}u^{\prime} \left(T)=0,\end{array}\right. where a∈L[0,T]a\in L\left[0,T] is sign-changing and the nonlinearity g:[0,∞)→Rg:{[}0,\infty )\to {\mathbb{R}} is continuous such that g(0)=g(1)=g(2)=0g\left(0)=g\left(1)=g\left(2)=0, g(s)>0g\left(s)\gt 0 for s∈(0,1)s\in \left(0,1), g(s)<0g\left(s)\lt 0 for s∈(1,2)s\in \left(1,2).https://doi.org/10.1515/math-2022-0062boundary value problemsign-changing weight functionpositive solutionsshooting method34b1534b18 |
| spellingShingle | Yue Xu Xiaoling Han Shooting method in the application of boundary value problems for differential equations with sign-changing weight function Open Mathematics boundary value problem sign-changing weight function positive solutions shooting method 34b15 34b18 |
| title | Shooting method in the application of boundary value problems for differential equations with sign-changing weight function |
| title_full | Shooting method in the application of boundary value problems for differential equations with sign-changing weight function |
| title_fullStr | Shooting method in the application of boundary value problems for differential equations with sign-changing weight function |
| title_full_unstemmed | Shooting method in the application of boundary value problems for differential equations with sign-changing weight function |
| title_short | Shooting method in the application of boundary value problems for differential equations with sign-changing weight function |
| title_sort | shooting method in the application of boundary value problems for differential equations with sign changing weight function |
| topic | boundary value problem sign-changing weight function positive solutions shooting method 34b15 34b18 |
| url | https://doi.org/10.1515/math-2022-0062 |
| work_keys_str_mv | AT yuexu shootingmethodintheapplicationofboundaryvalueproblemsfordifferentialequationswithsignchangingweightfunction AT xiaolinghan shootingmethodintheapplicationofboundaryvalueproblemsfordifferentialequationswithsignchangingweightfunction |