Abstract
The paper is devoted to the existence of solutions of initial value problems for nonlinear first order differential equations with nonlocal conditions. We shall rely on the Leray–Schauder fixed point principle to prove the main result. The novelty is a growth condition which is splitted into two parts, one for the subinterval containing the points involved by the nonlocal condition, and other for the rest of the interval.
Authors
Abdelkader Boucherif
Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals
Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals
Radu Precup
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania
Keywords
Nonlinear differential equation; Nonlocal initial condition; A priori bounds of solutions; Leray-Schauder fixed point principle.
Paper coordinates
A. Boucherif, R. Precup, On nonlocal initial value problem for first order differential equations, Fixed Point Theory 4 (2003) no. 2, 205-212.
About this paper
Journal
Fixed Point Theory
Publisher Name
paper on the journal website
Print ISSN
Online ISSN
MR 2031390, Zbl 105034001.
google scholar link
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[2] A. Boucherif, First-order differential inclusions with nonlocal initial conditions, Appl. Math. Letters 15 (2002), 409-414.
[3] L. Byszewski, Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem, J. Math. Anal. Appl. 162 (1991), 494-505.
[4] M. Frigon, Application de la theorie de la transversalite topologique a des problemes non lineaires pour desequations differentielles ordinaires, Dissertationes Math. 296, PWN, Warszawa, 1990.
[5] D. O’Regan and R. Precup, Theorems of Leray–Schauder Type and Applications, Gordon and Breach, Amsterdam, 2001 (Taylor and Francis, London, 2002).
[6] R. Precup, Methods in Nonlinear Integral Equations, Kluwer, Dordrecht–Boston–London, 2002.
[2] A. Boucherif, First-order differential inclusions with nonlocal initial conditions, Appl. Math. Letters 15 (2002), 409-414.
[3] L. Byszewski, Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem, J. Math. Anal. Appl. 162 (1991), 494-505.
[4] M. Frigon, Application de la theorie de la transversalite topologique a des problemes non lineaires pour desequations differentielles ordinaires, Dissertationes Math. 296, PWN, Warszawa, 1990.
[5] D. O’Regan and R. Precup, Theorems of Leray–Schauder Type and Applications, Gordon and Breach, Amsterdam, 2001 (Taylor and Francis, London, 2002).
[6] R. Precup, Methods in Nonlinear Integral Equations, Kluwer, Dordrecht–Boston–London, 2002.