Two positive solutions for nonlinear fourth-order elastic beam equations
The aim of this paper is to study the existence of at least two non-trivial solutions to a boundary value problem for fourth-order elastic beam equations given by \begin{align*} u^{(4)}+Au''+Bu = \lambda f(x,u) \quad \text{in } [0,1],\\ u(0) =u(1) = 0,\quad u''(0)=u'...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
University of Szeged
2019-05-01
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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=7532 |
| _version_ | 1827951182500331520 |
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| author | Giuseppina D'Aguì Beatrice Di Bella Patrick Winkert |
| author_facet | Giuseppina D'Aguì Beatrice Di Bella Patrick Winkert |
| author_sort | Giuseppina D'Aguì |
| collection | DOAJ |
| description | The aim of this paper is to study the existence of at least two non-trivial solutions to a boundary value problem for fourth-order elastic beam equations given by
\begin{align*}
u^{(4)}+Au''+Bu = \lambda f(x,u) \quad \text{in } [0,1],\\
u(0) =u(1) = 0,\quad
u''(0)=u''(1) = 0,
\end{align*}
under suitable conditions on the nonlinear term on the right hand side. Our approach is based on variational methods, and in particular, on an abstract two critical points theorem given for differentiable functionals defined on a real Banach space. |
| first_indexed | 2024-04-09T13:37:47Z |
| format | Article |
| id | doaj.art-e81e8b5357ee45c49ccda27869aa44ce |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:37:47Z |
| publishDate | 2019-05-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-e81e8b5357ee45c49ccda27869aa44ce2023-05-09T07:53:09ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752019-05-0120193711210.14232/ejqtde.2019.1.377532Two positive solutions for nonlinear fourth-order elastic beam equationsGiuseppina D'Aguì0Beatrice Di Bella1Patrick Winkert2University of Messina, Messina, ItalyUniversity of Messina, Messina, ItalyUniversity of Technology Berlin, Berlin, GermanyThe aim of this paper is to study the existence of at least two non-trivial solutions to a boundary value problem for fourth-order elastic beam equations given by \begin{align*} u^{(4)}+Au''+Bu = \lambda f(x,u) \quad \text{in } [0,1],\\ u(0) =u(1) = 0,\quad u''(0)=u''(1) = 0, \end{align*} under suitable conditions on the nonlinear term on the right hand side. Our approach is based on variational methods, and in particular, on an abstract two critical points theorem given for differentiable functionals defined on a real Banach space.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=7532critical pointsfourth-orderelastic beam equation |
| spellingShingle | Giuseppina D'Aguì Beatrice Di Bella Patrick Winkert Two positive solutions for nonlinear fourth-order elastic beam equations Electronic Journal of Qualitative Theory of Differential Equations critical points fourth-order elastic beam equation |
| title | Two positive solutions for nonlinear fourth-order elastic beam equations |
| title_full | Two positive solutions for nonlinear fourth-order elastic beam equations |
| title_fullStr | Two positive solutions for nonlinear fourth-order elastic beam equations |
| title_full_unstemmed | Two positive solutions for nonlinear fourth-order elastic beam equations |
| title_short | Two positive solutions for nonlinear fourth-order elastic beam equations |
| title_sort | two positive solutions for nonlinear fourth order elastic beam equations |
| topic | critical points fourth-order elastic beam equation |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=7532 |
| work_keys_str_mv | AT giuseppinadagui twopositivesolutionsfornonlinearfourthorderelasticbeamequations AT beatricedibella twopositivesolutionsfornonlinearfourthorderelasticbeamequations AT patrickwinkert twopositivesolutionsfornonlinearfourthorderelasticbeamequations |