The main purpose of this paper is to make Krasnoselskii’s compression-expansion fixed point theorem applicable to nonlinear integral equations in ordered Banach spaces
Department of Mathematics and Computer Science, North University of Baia Mare, Romania
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania
Nonlinear integral equations in abstract spaces; Krasnoselskii’s fixed point theorem.
A. Horvat-Marc, R. Precup, Nonnegative solutions of nonlinear integral equations in ordered Banach spaces, Fixed Point Theory, 5 (2004), 65-70.
Fixed Point Theory
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 R. Agarwal, M. Meehan, D. O’Regan and R. Precup, Location of nonnegative solutions for differential equation on finite and semi-infinite intervals, Dynamic Systems Appl. 12 (3-4) (2003), 323-341.
 L. H. Erbe, S. Hu and H. Wang, Multiple positive solutions of some boundary value problems, J. Math. Anal. Appl., 184 (1994), 640-648.
 L. H. Erbe and H. Wang, On the existence of positive solutions of ordinary differential equations, Proc. Amer. Math. Soc., 120 (1994), 743-748.
 D. Guo, V. Lakshmikantham and X. Liu, Nonlinear Integral Equation in Abstract Spaces, Kluwer Academic Publishers, Dordrecht-Boston-London, 1996.
 A. Horvat-Marc, Nonnegative solutions for boundary value problem, Bul. S¸tiint¸. Univ. Baia Mare, Ser. B, Mat.-Inf., 18 (2002), no. 2, 223-228.
 G. L. Karakostas and P. Ch. Tsamatos, Multiple positive solutions of some Fredholm integral equations arisen from nonlocal boundary-value problems, Electron. J. Differential Equations, 2002 (2002), no. 30, 1-17.
 M. A. Krasnoselskii, Positive Solutions of Operator Equations, Noordhoff, Groningen, 1964.
 W. Lian, F. Wong and C. Yeh, On the existence of positive solutions of nonlinear second order differential equations, Proc. Amer. Math. Soc., 124 (1996), 1117-1126.
 M. Meehan and D. O’Regan, Multiple nonnegative solutions of nonlinear integral equation on compact and semi-infinite intervals, Applicable Analysis, 74 (2000), 413-427.
 D. O’Regan and R. Precup, Theorems of Leray-Schauder Type and Applications, Gordon and Breach, Amsterdam, 2001.
 R. Precup, Methods in Nonlinear Integral Equations, Kluwer Academic Publishers, Dordrecht-Boston-London, 2002.
 J. Sun, H. Huo and W. Li, Positive solutions to singular nonlinear three point boundary value problems, Dynamic Systems Appl., 12 (3-4) (2003), 275-283.