| Title:
|
On some boundary value problems for second order nonlinear differential equations (English) |
| Author:
|
Došlá, Zuzana |
| Author:
|
Marini, Mauro |
| Author:
|
Matucci, Serena |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
137 |
| Issue:
|
2 |
| Year:
|
2012 |
| Pages:
|
113-122 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We investigate two boundary value problems for the second order differential equation with $p$-Laplacian \[ (a(t)\Phi _{p}(x'))'=b(t)F(x), \quad t\in I=[0,\infty ), \] where $a$, $b$ are continuous positive functions on $I$. We give necessary and sufficient conditions which guarantee the existence of a unique (or at least one) positive solution, satisfying one of the following two boundary conditions: \[ {\rm i)}\ x(0)=c>0, \ \lim _{t\rightarrow \infty }x(t)=0; \quad {\rm ii)}\ x'(0)=d<0, \ \lim _{t\rightarrow \infty }x(t)=0. \] (English) |
| Keyword:
|
boundary value problem |
| Keyword:
|
$p$-Laplacian |
| Keyword:
|
half-linear equation |
| Keyword:
|
positive solution |
| Keyword:
|
uniqueness |
| Keyword:
|
decaying solution |
| Keyword:
|
principal solution |
| MSC:
|
34B18 |
| MSC:
|
34B40 |
| MSC:
|
34C10 |
| MSC:
|
34D05 |
| idZBL:
|
Zbl 1265.34113 |
| idMR:
|
MR2978257 |
| DOI:
|
10.21136/MB.2012.142856 |
| . |
| Date available:
|
2012-06-08T10:04:34Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/142856 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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