Remarks on existence of positive solutions of some integral equations
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2005)
- Volume: 44, Issue: 1, page 71-82
- ISSN: 0231-9721
Access Full Article
top
Abstract
topHow to cite
topLigęza, Jan. "Remarks on existence of positive solutions of some integral equations." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 44.1 (2005): 71-82. <http://eudml.org/doc/32452>.
@article{Ligęza2005,
abstract = {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.},
author = {Ligęza, Jan},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {Positive solutions; Fredholm integral equations; cone; boundary value problems; fixed point theorem; positive solution; nonlinear integral equation},
language = {eng},
number = {1},
pages = {71-82},
publisher = {Palacký University Olomouc},
title = {Remarks on existence of positive solutions of some integral equations},
url = {http://eudml.org/doc/32452},
volume = {44},
year = {2005},
}
TY - JOUR
AU - Ligęza, Jan
TI - Remarks on existence of positive solutions of some integral equations
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2005
PB - Palacký University Olomouc
VL - 44
IS - 1
SP - 71
EP - 82
AB - 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.
LA - eng
KW - Positive solutions; Fredholm integral equations; cone; boundary value problems; fixed point theorem; positive solution; nonlinear integral equation
UR - http://eudml.org/doc/32452
ER -
References
top- Agarwal R. P., Grace S. R., O’Regan D., Existence of positive solutions of semipositone Fredholm integral equation, Funkciałaj Equaciaj 45 (2002), 223–235. MR1948600
- Agarwal R. P., O’Regan D.: Infinite Interval Problems For Differential, Difference, Integral Equations., Kluwer Acad. Publishers, Dordrecht, Boston, London, , 2001. MR1845855
- Agarwal R. P., O’Regan D., Wang J. Y.: Positive Solutions of Differential, Difference, Integral Equations., Kluwer Academic Publishers, Dordrecht, Boston, London, , 1999. (1999) MR1680024
- Deimling K.: Nonlinear Functional Analysis., Springer, New York, , 1985. (1985) MR0787404
- Guo D., Lakshmikannthan V.: Nonlinear Problems in Abstract Cones., Academic Press, San Diego, , 1988. (1988) MR0959889
- Galewski A., On a certain generalization of the Krasnosielskii theorem, J. Appl. Anal. 1 (2003), 139–147.
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.