| Title:
|
Boundary value problem with an inner point for the singularly perturbed semilinear differential equations (English) |
| Author:
|
Vrábeľ, Róbert |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
136 |
| Issue:
|
1 |
| Year:
|
2011 |
| Pages:
|
1-8 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we investigate the problem of existence and asymptotic behavior of solutions for the nonlinear boundary value problem $$ \epsilon y''+ky=f(t,y),\quad t\in \langle a,b \rangle , \ k<0,\ 0<\epsilon \ll 1 $$ satisfying three point boundary conditions. Our analysis relies on the method of lower and upper solutions and delicate estimations. (English) |
| Keyword:
|
singular perturbation |
| Keyword:
|
boundary value problem |
| Keyword:
|
upper solution |
| Keyword:
|
lower solution |
| MSC:
|
34B10 |
| MSC:
|
34B16 |
| MSC:
|
34E05 |
| MSC:
|
34E10 |
| MSC:
|
34E20 |
| idZBL:
|
Zbl 1224.34037 |
| idMR:
|
MR2807703 |
| DOI:
|
10.21136/MB.2011.141442 |
| . |
| Date available:
|
2011-03-31T11:19:12Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141442 |
| . |
| Reference:
|
[1] Coster, C. De, Habets, P.: Two-Point Boundary Value Problems: Lower and Upper Solutions.Volume 205 (Mathematics in Science and Engineering), Elsevier (2006). MR 2225284 |
| Reference:
|
[2] Mawhin, J.: Points fixes, points critiques et problemes aux limites.Semin. Math. Sup. no. 92, Presses Univ. Montreal (1985). Zbl 0561.34001, MR 0789982 |
| Reference:
|
[3] Šeda, V.: On some non-linear boundary value problems for ordinary differential equations.Arch. Math., Brno {\it 25} (1989), 207-222. MR 1188065 |
| Reference:
|
[4] Vrábeľ, R.: Asymptotic behavior of T-periodic solutions of singularly perturbed second-order differential equation.Math. Bohem. 121 (1996), 73-76. MR 1388177 |
| Reference:
|
[5] Vrábeľ, R.: Semilinear singular perturbation.Nonlin. Anal. Theory Methods Appl. 25 (1995), 17-26. MR 1331985, 10.1016/0362-546X(94)00123-Y |
| . |
