| Title:
|
An existence theorem of positive solutions to a singular nonlinear boundary value problem (English) |
| Author:
|
Bonanno, Gabriele |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
36 |
| Issue:
|
4 |
| Year:
|
1995 |
| Pages:
|
609-614 |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this note we consider the boundary value problem $y''=f(x,y,y')$ $\,(x\in [0,X];X>0)$, $y(0)=0$, $y(X)=a>0$; where $f$ is a real function which may be singular at $y=0$. We prove an existence theorem of positive solutions to the previous problem, under different hypotheses of Theorem 2 of L.E. Bobisud [J. Math. Anal. Appl. 173 (1993), 69–83], that extends and improves Theorem 3.2 of D. O'Regan [J. Differential Equations 84 (1990), 228–251]. (English) |
| Keyword:
|
ordinary differential equations |
| Keyword:
|
singular boundary value problem |
| Keyword:
|
positive solutions |
| MSC:
|
34B15 |
| idZBL:
|
Zbl 0847.34020 |
| idMR:
|
MR1378684 |
| . |
| Date available:
|
2009-01-08T18:20:31Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118790 |
| . |
| Reference:
|
[1] Arino O., Gautier S., Penot J.P.: A fixed point theorem for sequentially continuous mappings with application to ordinary differential equations.Funkcial. Ekv. 27 (1984), 273-279. Zbl 0599.34008, MR 0794756 |
| Reference:
|
[2] Bobisud L.E.: Existence of positive solutions to some nonlinear singular boundary value problems on finite and infinite intervals.J. Math. Anal. Appl. 173 (1993), 69-83. Zbl 0777.34017, MR 1205910 |
| Reference:
|
[3] Diestel J., Uhl J.J.: Vector Measures.Math. Survey, no. 15, Amer. Soc., 1977. Zbl 0521.46035, MR 0453964 |
| Reference:
|
[4] O'Regan D.: Existence of positive solutions to some singular and nonsingular second order boundary value problems.J. Differential Equations 84 (1990), 228-251. Zbl 0706.34030, MR 1047568 |
| . |
