| Title:
|
Positive solutions and eigenvalue intervals of a nonlinear singular fourth-order boundary value problem (English) |
| Author:
|
Yao, Qingliu |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
58 |
| Issue:
|
1 |
| Year:
|
2013 |
| Pages:
|
93-110 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We consider the classical nonlinear fourth-order two-point boundary value problem $$ \begin {cases} u^{(4)}(t)=\lambda h(t)f(t,u(t),u'(t),u''(t)),\quad 0<t<1,\\ u(0)=u'(1)=u''(0)=u'''(1)=0. \end {cases} $$ In this problem, the nonlinear term $h(t)f(t,u(t),u'(t),u''(t))$ contains the first and second derivatives of the unknown function, and the function $h(t)f(t,x,y,z)$ may be singular at $t=0$, $t=1$ and at $x=0$, $y=0$, $z=0$. By introducing suitable height functions and applying the fixed point theorem on the cone, we establish several local existence theorems on positive solutions and obtain the corresponding eigenvalue intervals. (English) |
| Keyword:
|
nonlinear ordinary differential equation |
| Keyword:
|
singular nonlinearity |
| Keyword:
|
positive solution |
| Keyword:
|
eigenvalue interval |
| MSC:
|
34B08 |
| MSC:
|
34B09 |
| MSC:
|
34B15 |
| MSC:
|
34B16 |
| MSC:
|
34B18 |
| MSC:
|
34B27 |
| MSC:
|
34L15 |
| MSC:
|
47N20 |
| idZBL:
|
Zbl 1274.34076 |
| idMR:
|
MR3022770 |
| DOI:
|
10.1007/s10492-013-0004-8 |
| . |
| Date available:
|
2013-01-23T10:14:49Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143136 |
| . |
| Reference:
|
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