Article
| 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 |
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| Category: | math |
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| 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 |
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| Date available: | 2023-05-04T17:41:04Z |
| Last updated: | 2023-09-13 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/151659 |
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