On the fourth-order nonlinear beam equation of a small deflection with nonlocal conditions
$ {equation*} u^{(4)}+A(x)u = \lambda f (x, \ u, \ u''), \ 0<x<1 {equation*} $ subject to the integral boundary conditions: $ {equation*} u(0) = u(1) = \int_{0}^{1}p(x)u(x)dx, \ u''(0) = u''(1) = \int_{0}^{1}q(x)u''(x)dx, {equation*} $...
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AIMS Press
2021-07-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://aimspress.com/article/doi/10.3934/math.2021575?viewType=HTML |
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doaj-51c6e48ab0b1464ba08053f2ceaa64d42021-07-21T02:44:40ZengAIMS PressAIMS Mathematics2473-69882021-07-01699899991010.3934/math.2021575On the fourth-order nonlinear beam equation of a small deflection with nonlocal conditionsAmmar Khanfer0Lazhar Bougoffa11. Department of Mathematics and General Sciences, Prince Sultan University, Riyadh, Saudi Arabia2. Department of Mathematics and Statistics, Imam Mohammad Ibn Saud Islamic University (IMSIU), P.O. Box 90950, Riyadh 11623, Saudi Arabia $ {equation*} u^{(4)}+A(x)u = \lambda f (x, \ u, \ u''), \ 0<x<1 {equation*} $ subject to the integral boundary conditions: $ {equation*} u(0) = u(1) = \int_{0}^{1}p(x)u(x)dx, \ u''(0) = u''(1) = \int_{0}^{1}q(x)u''(x)dx, {equation*} $ where $ A\in \mathbb{C}[0, 1], $ $ \lambda > 0 $ is a parameter and $ p, q \in \mathbb{L}^{1}[0, 1]. $ https://aimspress.com/article/doi/10.3934/math.2021575?viewType=HTMLfourth-order beam equationnonlocal boundary conditionsexistence and uniqueness theoremschauder's fixed point theorem |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Ammar Khanfer Lazhar Bougoffa |
| spellingShingle |
Ammar Khanfer Lazhar Bougoffa On the fourth-order nonlinear beam equation of a small deflection with nonlocal conditions AIMS Mathematics fourth-order beam equation nonlocal boundary conditions existence and uniqueness theorem schauder's fixed point theorem |
| author_facet |
Ammar Khanfer Lazhar Bougoffa |
| author_sort |
Ammar Khanfer |
| title |
On the fourth-order nonlinear beam equation of a small deflection with nonlocal conditions |
| title_short |
On the fourth-order nonlinear beam equation of a small deflection with nonlocal conditions |
| title_full |
On the fourth-order nonlinear beam equation of a small deflection with nonlocal conditions |
| title_fullStr |
On the fourth-order nonlinear beam equation of a small deflection with nonlocal conditions |
| title_full_unstemmed |
On the fourth-order nonlinear beam equation of a small deflection with nonlocal conditions |
| title_sort |
on the fourth-order nonlinear beam equation of a small deflection with nonlocal conditions |
| publisher |
AIMS Press |
| series |
AIMS Mathematics |
| issn |
2473-6988 |
| publishDate |
2021-07-01 |
| description |
$ {equation*} u^{(4)}+A(x)u = \lambda f (x, \ u, \ u''), \ 0<x<1 {equation*} $
subject to the integral boundary conditions:
$ {equation*} u(0) = u(1) = \int_{0}^{1}p(x)u(x)dx, \ u''(0) = u''(1) = \int_{0}^{1}q(x)u''(x)dx, {equation*} $
where $ A\in \mathbb{C}[0, 1], $ $ \lambda > 0 $ is a parameter and $ p, q \in \mathbb{L}^{1}[0, 1]. $
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| topic |
fourth-order beam equation nonlocal boundary conditions existence and uniqueness theorem schauder's fixed point theorem |
| url |
https://aimspress.com/article/doi/10.3934/math.2021575?viewType=HTML |
| work_keys_str_mv |
AT ammarkhanfer onthefourthordernonlinearbeamequationofasmalldeflectionwithnonlocalconditions AT lazharbougoffa onthefourthordernonlinearbeamequationofasmalldeflectionwithnonlocalconditions |
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1721293159472824320 |