| Title:
|
A priori bounds for positive radial solutions of quasilinear equations of Lane–Emden type (English) |
| Author:
|
Bae, Soohyun |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
59 |
| Issue:
|
2 |
| Year:
|
2023 |
| Pages:
|
155-162 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We consider the quasilinear equation $\Delta _p u +K(|x|)u^q=0$, and present the proof of the local existence of positive radial solutions near $0$ under suitable conditions on $K$. Moreover, we provide a priori estimates of positive radial solutions near $\infty $ when $r^{-\ell }K(r)$ for $\ell \ge -p$ is bounded near $\infty $. (English) |
| Keyword:
|
quasilinear equation |
| Keyword:
|
positive solution |
| Keyword:
|
a priori bound |
| MSC:
|
35B45 |
| MSC:
|
35J92 |
| idZBL:
|
Zbl 07675585 |
| idMR:
|
MR4563027 |
| DOI:
|
10.5817/AM2023-2-155 |
| . |
| Date available:
|
2023-02-22T14:39:44Z |
| Last updated:
|
2023-05-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/151562 |
| . |
| Reference:
|
[1] Bidaut-Véron, M.-F., Pohozaev, S.: Nonexistence results and estimates for some nonlinear elliptic problems.J. Anal. Math. 84 (2001), 1–49. MR 1849197, 10.1007/BF02788105 |
| Reference:
|
[2] Kawano, N., Ni, W.-M., Yotsutani, S.: A generalized Pohozaev identity and its applications.J. Math. Soc. Japan 42 (1990), 541–564. 10.2969/jmsj/04230541 |
| Reference:
|
[3] Kawano, N., Yanagida, E., Yotsutani, S.: Structure theorems for positive radial solutions to ${\rm div} (|D u|^{m-2}D u) + K(|x|)u^q=0$ in ${\bf R}^n$.J. Math. Soc. Japan 45 (1993), 719–742. |
| Reference:
|
[4] Li, Y., Ni, W.-M.: On conformal scalar curvature equation in ${\bf R}^n$.Duke Math. J. 57 (1988), 895–924. |
| Reference:
|
[5] Ni, W.-M., Serrin, J.: Existence and non-existence theorems for ground states of quasilinear partial differential equations: The anomalous case.Atti Convegni Lincei 77 (1986), 231–257. |
| Reference:
|
[6] Serrin, J., Zou, H.: Cauchy-Liouville and universal boundedness theorems for quasilinear elliptic equations and inequalities.Acta Math. 189 (2002), 79–142. MR 1946918, 10.1007/BF02392645 |
| . |
