| Title:
|
Global structure of positive solutions for superlinear $2m$th-boundary value problems (English) |
| Author:
|
Ma, Ruyun |
| Author:
|
An, Yulian |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
60 |
| Issue:
|
1 |
| Year:
|
2010 |
| Pages:
|
161-172 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We consider boundary value problems for nonlinear $2m$th-order eigenvalue problem $$ \begin{aligned} (-1)^mu^{(2m)}(t)&=\lambda a(t)f(u(t)),\ \ \ \ \ 0<t<1, \\ u^{(2i)}(0)&=u^{(2i)}(1)=0,\ \ \ \ i=0,1,2,\cdots ,m-1 . \end{aligned} $$ where $a\in C([0,1], [0,\infty ))$ and $a(t_0)>0$ for some $t_0\in [0,1]$, $f\in C([0,\infty ),[0,\infty ))$ and $f(s)>0$ for $s>0$, and $f_0=\infty $, where $f_0=\lim _{s\rightarrow 0^+}f(s)/s$. We investigate the global structure of positive solutions by using Rabinowitz's global bifurcation theorem. (English) |
| Keyword:
|
multiplicity results |
| Keyword:
|
Lidstone boundary value problem |
| Keyword:
|
eigenvalues |
| Keyword:
|
bifurcation methods |
| Keyword:
|
positive solutions |
| MSC:
|
34B08 |
| MSC:
|
34B10 |
| MSC:
|
34B18 |
| MSC:
|
34G20 |
| MSC:
|
47J15 |
| MSC:
|
47N20 |
| idZBL:
|
Zbl 1224.34034 |
| idMR:
|
MR2595080 |
| . |
| Date available:
|
2010-07-20T16:24:35Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140559 |
| . |
| Reference:
|
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