Global structure of one-sign solutions for a simply supported beam equation
Abstract In this paper, we consider the nonlinear eigenvalue problem u ′′′′ = λ h ( t ) f ( u ) , 0 < t < 1 , u ( 0 ) = u ( 1 ) = u ″ ( 0 ) = u ″ ( 1 ) = 0 , $$\begin{gathered} u''''= \lambda h(t)f(u),\quad 0< t< 1, \\ u(0)=u(1)=u''(0)=u''(1)=0, \\...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-04-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13660-020-02376-y |
| _version_ | 1818610784863780864 |
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| author | Dongliang Yan Ruyun Ma Xiaoxiao Su |
| author_facet | Dongliang Yan Ruyun Ma Xiaoxiao Su |
| author_sort | Dongliang Yan |
| collection | DOAJ |
| description | Abstract In this paper, we consider the nonlinear eigenvalue problem u ′′′′ = λ h ( t ) f ( u ) , 0 < t < 1 , u ( 0 ) = u ( 1 ) = u ″ ( 0 ) = u ″ ( 1 ) = 0 , $$\begin{gathered} u''''= \lambda h(t)f(u),\quad 0< t< 1, \\ u(0)=u(1)=u''(0)=u''(1)=0, \\ \end{gathered} $$ where h ∈ C ( [ 0 , 1 ] , ( 0 , ∞ ) ) $h\in C([0,1], (0,\infty))$ ; f ∈ C ( R , R ) $f\in C(\mathbb{R},\mathbb{R})$ and s f ( s ) > 0 $sf(s)>0$ for s ≠ 0 $s\neq0$ , and f 0 = f ∞ = 0 $f_{0}=f_{\infty}=0$ , f 0 = lim | s | → 0 f ( s ) / s $f_{0}=\lim_{|s|\rightarrow0}f(s)/s$ , f ∞ = lim | s | → ∞ f ( s ) / s $f_{\infty}=\lim_{|s|\rightarrow\infty}f(s)/s$ . We investigate the global structure of one-sign solutions by using bifurcation techniques. |
| first_indexed | 2024-12-16T15:19:57Z |
| format | Article |
| id | doaj.art-e1b4bddca2444de0ab6e0f50f3fd318c |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-12-16T15:19:57Z |
| publishDate | 2020-04-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-e1b4bddca2444de0ab6e0f50f3fd318c2022-12-21T22:26:40ZengSpringerOpenJournal of Inequalities and Applications1029-242X2020-04-012020111110.1186/s13660-020-02376-yGlobal structure of one-sign solutions for a simply supported beam equationDongliang Yan0Ruyun Ma1Xiaoxiao Su2Department of Mathematics, Northwest Normal UniversityDepartment of Mathematics, Northwest Normal UniversityDepartment of Mathematics, Northwest Normal UniversityAbstract In this paper, we consider the nonlinear eigenvalue problem u ′′′′ = λ h ( t ) f ( u ) , 0 < t < 1 , u ( 0 ) = u ( 1 ) = u ″ ( 0 ) = u ″ ( 1 ) = 0 , $$\begin{gathered} u''''= \lambda h(t)f(u),\quad 0< t< 1, \\ u(0)=u(1)=u''(0)=u''(1)=0, \\ \end{gathered} $$ where h ∈ C ( [ 0 , 1 ] , ( 0 , ∞ ) ) $h\in C([0,1], (0,\infty))$ ; f ∈ C ( R , R ) $f\in C(\mathbb{R},\mathbb{R})$ and s f ( s ) > 0 $sf(s)>0$ for s ≠ 0 $s\neq0$ , and f 0 = f ∞ = 0 $f_{0}=f_{\infty}=0$ , f 0 = lim | s | → 0 f ( s ) / s $f_{0}=\lim_{|s|\rightarrow0}f(s)/s$ , f ∞ = lim | s | → ∞ f ( s ) / s $f_{\infty}=\lim_{|s|\rightarrow\infty}f(s)/s$ . We investigate the global structure of one-sign solutions by using bifurcation techniques.http://link.springer.com/article/10.1186/s13660-020-02376-yConnected componentGreen functionOne-sign solutionsBifurcationSimply supported beam |
| spellingShingle | Dongliang Yan Ruyun Ma Xiaoxiao Su Global structure of one-sign solutions for a simply supported beam equation Journal of Inequalities and Applications Connected component Green function One-sign solutions Bifurcation Simply supported beam |
| title | Global structure of one-sign solutions for a simply supported beam equation |
| title_full | Global structure of one-sign solutions for a simply supported beam equation |
| title_fullStr | Global structure of one-sign solutions for a simply supported beam equation |
| title_full_unstemmed | Global structure of one-sign solutions for a simply supported beam equation |
| title_short | Global structure of one-sign solutions for a simply supported beam equation |
| title_sort | global structure of one sign solutions for a simply supported beam equation |
| topic | Connected component Green function One-sign solutions Bifurcation Simply supported beam |
| url | http://link.springer.com/article/10.1186/s13660-020-02376-y |
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