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'...
| Published in: | Electronic Journal of Qualitative Theory of Differential Equations |
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| Main Authors: | , , |
| Format: | Article |
| Language: | English |
| Published: |
University of Szeged
2019-05-01
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| Subjects: | |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=7532 |
| Summary: | 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. |
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| ISSN: | 1417-3875 |