| 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:
|
http://hdl.handle.net/10338.dmlcz/141766 |
| . |
| Reference:
|
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