| Title:
|
Remarks on existence of positive solutions of some integral equations (English) |
| Author:
|
Ligęza, Jan |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
44 |
| Issue:
|
1 |
| Year:
|
2005 |
| Pages:
|
71-82 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We study the existence of positive solutions of the integral equation \[ x(t) = \mu \int _0^1 k(t, s) f(s, x(s), x^{\prime }(s), \ldots , x^{(n-1)} (s))\, ds, \quad n \ge 2 \] in both $ C^{n-1} [0, 1] $ and $ W^{n-1, p} [0, 1] $ spaces, where $ p \ge 1 $ and $ \mu > 0 $. Throughout this paper $k$ is nonnegative but the nonlinearity $f$ may take negative values. The Krasnosielski fixed point theorem on cone is used. (English) |
| Keyword:
|
Positive solutions |
| Keyword:
|
Fredholm integral equations |
| Keyword:
|
cone |
| Keyword:
|
boundary value problems |
| Keyword:
|
fixed point theorem. |
| MSC:
|
34B10 |
| MSC:
|
34B15 |
| MSC:
|
34G20 |
| MSC:
|
34K10 |
| MSC:
|
45B05 |
| MSC:
|
45G10 |
| MSC:
|
45M20 |
| idZBL:
|
Zbl 1090.45005 |
| idMR:
|
MR2218569 |
| . |
| Date available:
|
2009-08-21T06:50:48Z |
| Last updated:
|
2012-05-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133384 |
| . |
| Reference:
|
[1] Agarwal R. P., Grace S. R., O’Regan D.: Existence of positive solutions of semipositone Fredholm integral equation.Funkciałaj Equaciaj 45 (2002), 223–235. MR 1948600 |
| Reference:
|
[2] Agarwal R. P., O’Regan D.: Infinite Interval Problems For Differential, Difference, Integral Equations. : Kluwer Acad. Publishers, Dordrecht, Boston, London., 2001. MR 1845855 |
| Reference:
|
[3] Agarwal R. P., O’Regan D., Wang J. Y.: Positive Solutions of Differential, Difference, Integral Equations. : Kluwer Academic Publishers, Dordrecht, Boston, London., 1999. MR 1680024 |
| Reference:
|
[4] Deimling K.: Nonlinear Functional Analysis. : Springer, New York., 1985. MR 0787404 |
| Reference:
|
[5] Guo D., Lakshmikannthan V.: Nonlinear Problems in Abstract Cones. : Academic Press, San Diego., 1988. MR 0959889 |
| Reference:
|
[6] Galewski A.: On a certain generalization of the Krasnosielskii theorem.J. Appl. Anal. 1 (2003), 139–147. |
| . |
