Author:
Harjani J.,López B.,Sadarangani K.
Abstract
AbstractIn the present paper, by using the mixed monotone operator method we prove the existence and uniqueness of positive solution to the following cantilever-type boundary value problem $$\begin{aligned} \displaystyle \left\{ \begin{array}{l} u^{(4)}(t)=f(t,u(t),u(\alpha t))+g(t,u(t)),\quad 0<t<1, \quad \alpha \in (0,1),\\ u(0)=u'(0)=u''(1)=u'''(1)=0. \end{array}\right. \end{aligned}$$
u
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4
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f
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t
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u
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u
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t
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g
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t
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u
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0
<
t
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1
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α
∈
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0
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1
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u
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0
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=
u
′
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0
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=
u
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1
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u
′
′
′
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1
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=
0
.
Moreover, in order to illustrate the results we present an example.
Funder
Universidad de las Palmas de Gran Canaria
Publisher
Springer Science and Business Media LLC
Subject
General Mathematics,Theoretical Computer Science,Analysis
Reference15 articles.
1. Anderson, D.R., Hoffacker, J.: Existence of solutions for a cantilever beam problem. J. Math. Anal. Appl. 323(2), 958–973 (2006)
2. Li, Y.: Existence of positive solutions for the cantilever beam equations with fully nonlinear terms. Nonlinear Anal. RWA 27, 221–237 (2016)
3. Yao, Q.: Monotonically iterative method of nonlinear cantilever beam equations. Appl. Math. Comput. 205(1), 432–437 (2008)
4. Guo, D., Lakshmikantham, V.: Coupled fixed points of nonlinear operators with applications. Nonlinear Anal. 11, 623–631 (1987)
5. Guo, D.: Fixed points of mixed monotone operators with application. Appl. Anal. 34, 215–224 (1988)