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Title: Solvability of a class of elastic beam equations with strong Carathéodory nonlinearity (English)
Author: Yao, Qingliu
Language: English
Journal: Applications of Mathematics
ISSN: 0862-7940 (print)
ISSN: 1572-9109 (online)
Volume: 56
Issue: 6
Year: 2011
Pages: 543-555
Summary lang: English
Category: math
Summary: We study the existence of a solution to the nonlinear fourth-order elastic beam equation with nonhomogeneous boundary conditions \[ \begin {cases} u^{(4)}(t)=f\bigl (t,u(t),u'(t),u''(t),u'''(t)\bigr ),\quad \text {a.e.} \ t\in [0,1],\\ u(0)=a, \ u'(0)=b, \ u(1)=c, \ u''(1)=d, \end {cases} \] where the nonlinear term $f(t,u_{0},u_{1},u_{2},u_{3})$ is a strong Carathéodory function. By constructing suitable height functions of the nonlinear term $f(t,u_{0},u_{1},u_{2},u_{3})$ on bounded sets and applying the Leray-Schauder fixed point theorem, we prove that the equation has a solution provided that the integration of some height function has an appropriate value. (English)
Keyword: nonlinear ordinary differential equation
Keyword: boundary value problem
Keyword: existence
Keyword: fixed point theorem
MSC: 34B15
MSC: 34B16
MSC: 47N20
MSC: 74K10
idZBL: Zbl 1249.34064
idMR: MR2886237
DOI: 10.1007/s10492-011-0032-1
Date available: 2011-12-16T15:05:13Z
Last updated: 2020-07-02
Stable URL:
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