| Title:
|
Upper and lower solutions for singularly perturbed semilinear Neumann's problem (English) |
| Author:
|
Vrábeľ, Róbert |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
122 |
| Issue:
|
2 |
| Year:
|
1997 |
| Pages:
|
175-180 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The paper establishes sufficient conditions for the existence of solutions of Neumann's problem for the differential equation $\mu y"+ky=f(t,y)$ which tend to the solution of the reduced problem $ky=f(t,y)$ on $[0,1]$ as $\mu\to0.$ (English) |
| Keyword:
|
singularly perturbed equation |
| Keyword:
|
Neumann’s problem |
| MSC:
|
34B15 |
| MSC:
|
34E15 |
| MSC:
|
34E20 |
| MSC:
|
35B10 |
| idZBL:
|
Zbl 0893.34052 |
| idMR:
|
MR1460947 |
| DOI:
|
10.21136/MB.1997.125912 |
| . |
| Date available:
|
2009-09-24T21:24:43Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/125912 |
| . |
| Reference:
|
[1] R. E. O'Malley, Jr.: Phase-plane solutions to some singular perturbation problems.J. Math. Anal. Appl. 54, (1976), 449-466. Zbl 0334.34050, MR 0450722, 10.1016/0022-247X(76)90214-6 |
| Reference:
|
[2] J. Mawhin: Points fixes, points critiques ct problemes aux limites.Sémin. Math. Sup. no. 92, Presses Univ. Montгéal, Montréal, 1985. MR 0789982 |
| Reference:
|
[3] K. W. Chang F. A. Howes: Nonlinear singular perturbation phenomena.Springer-Verlag, 1984. MR 0764395 |
| . |
