Multiplicity of nodal solutions for fourth order equation with clamped beam boundary conditions
In this paper, we study the global structure of nodal solutions of $$ \begin{cases} u''''(x)=\lambda h(x)f(u(x)), & 0<x<1, \\ u(0)=u(1)=u'(0)=u'(1)=0,\\ \end{cases}$$ where $\lambda > 0$ is a parameter, $h\in C([0,1],(0, \infty))$, $f\in C(\mathbb{R})$ and...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
University of Szeged
2020-12-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Subjects: | |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=8936 |
| _version_ | 1797830537823387648 |
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| author | Ruyun Ma Dongliang Yan Liping Wei |
| author_facet | Ruyun Ma Dongliang Yan Liping Wei |
| author_sort | Ruyun Ma |
| collection | DOAJ |
| description | In this paper, we study the global structure of nodal solutions of
$$
\begin{cases}
u''''(x)=\lambda h(x)f(u(x)), & 0<x<1, \\
u(0)=u(1)=u'(0)=u'(1)=0,\\
\end{cases}$$
where $\lambda > 0$ is a parameter, $h\in C([0,1],(0, \infty))$, $f\in C(\mathbb{R})$ and $sf(s)>0$ for $|s|>0$. We show the existence of $S$-shaped component of nodal solutions for the above problem. The proof is based on the bifurcation technique. |
| first_indexed | 2024-04-09T13:37:42Z |
| format | Article |
| id | doaj.art-cf6f309ca0914acb8094a2fc3a37f566 |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:37:42Z |
| publishDate | 2020-12-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-cf6f309ca0914acb8094a2fc3a37f5662023-05-09T07:53:10ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752020-12-0120208511410.14232/ejqtde.2020.1.858936Multiplicity of nodal solutions for fourth order equation with clamped beam boundary conditionsRuyun Ma0Dongliang Yan1Liping Wei2Department of Mathematics, Northwest Normal University, Lanzhou, P.R. ChinaNorthwest Normal University, Lanzhou, P.R. ChinaNorthwest Normal University, Lanzhou, P.R. ChinaIn this paper, we study the global structure of nodal solutions of $$ \begin{cases} u''''(x)=\lambda h(x)f(u(x)), & 0<x<1, \\ u(0)=u(1)=u'(0)=u'(1)=0,\\ \end{cases}$$ where $\lambda > 0$ is a parameter, $h\in C([0,1],(0, \infty))$, $f\in C(\mathbb{R})$ and $sf(s)>0$ for $|s|>0$. We show the existence of $S$-shaped component of nodal solutions for the above problem. The proof is based on the bifurcation technique.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=8936clamped beamfourth order equationsconnected componentnodal solutionsbifurcation |
| spellingShingle | Ruyun Ma Dongliang Yan Liping Wei Multiplicity of nodal solutions for fourth order equation with clamped beam boundary conditions Electronic Journal of Qualitative Theory of Differential Equations clamped beam fourth order equations connected component nodal solutions bifurcation |
| title | Multiplicity of nodal solutions for fourth order equation with clamped beam boundary conditions |
| title_full | Multiplicity of nodal solutions for fourth order equation with clamped beam boundary conditions |
| title_fullStr | Multiplicity of nodal solutions for fourth order equation with clamped beam boundary conditions |
| title_full_unstemmed | Multiplicity of nodal solutions for fourth order equation with clamped beam boundary conditions |
| title_short | Multiplicity of nodal solutions for fourth order equation with clamped beam boundary conditions |
| title_sort | multiplicity of nodal solutions for fourth order equation with clamped beam boundary conditions |
| topic | clamped beam fourth order equations connected component nodal solutions bifurcation |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=8936 |
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