| Title:
|
$S$-shaped component of nodal solutions for problem involving one-dimension mean curvature operator (English) |
| Author:
|
Ma, Ruyun |
| Author:
|
He, Zhiqian |
| Author:
|
Su, Xiaoxiao |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
73 |
| Issue:
|
2 |
| Year:
|
2023 |
| Pages:
|
321-333 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $E=\{u\in C^1[0,1] \colon u(0)=u(1)=0\}$. Let $S_k^\nu $ with $\nu =\{+, -\}$ denote the set of functions $u\in E$ which have exactly $k-1$ interior nodal zeros in (0, 1) and $\nu u$ be positive near $0$. We show the existence of $S$-shaped connected component of $S_k^\nu $-solutions of the problem $$ \begin{cases} \biggl (\dfrac {u'}{\sqrt {1-u'^2}}\bigg )^{\prime }+\lambda a(x) f(u)=0, & x\in (0,1), \\ u(0)=u(1)=0, & \end{cases} $$ where $\lambda >0$ is a parameter, $a\in C([0, 1], (0,\infty ))$. We determine the intervals of parameter $\lambda $ in which the above problem has one, two or three $S_k^\nu $-solutions. The proofs of the main results are based upon the bifurcation technique. (English) |
| Keyword:
|
mean curvature operator |
| Keyword:
|
$S_k^\nu $-solution |
| Keyword:
|
bifurcation |
| Keyword:
|
Sturm-type comparison theorem |
| MSC:
|
34C10 |
| MSC:
|
34C23 |
| MSC:
|
35B40 |
| MSC:
|
35J65 |
| idZBL:
|
Zbl 07729510 |
| idMR:
|
MR4586897 |
| DOI:
|
10.21136/CMJ.2023.0027-20 |
| . |
| Date available:
|
2023-05-04T17:41:04Z |
| Last updated:
|
2025-07-07 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/151659 |
| . |
| Reference:
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