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Title: Existence of nondecreasing and continuous solutions of an integral equation with linear modification of the argument
Authors: Caballero, J. 
López, B. 
Sadarangani, K. 
UNESCO Clasification: 120215 Ecuaciones integrales
120219 Ecuaciones diferenciales ordinarias
1202 Análisis y análisis funcional
Keywords: Measure of noncompactness
Fixed point theorem
Nondecreasing solutions
Issue Date: 2007
Journal: Acta Mathematica Sinica, English Series 
Abstract: We use a technique associated with measures of noncompactness to prove the existence of nondecreasing solutions to an integral equation with linear modi. cation of the argument in the space C[ 0, 1]. In the last thirty years there has been a great deal of work in the field of differential equations with a modified argument. A special class is represented by the differential equation with affine modification of the argument which can be delay differential equations or differential equations with linear modi. cations of the argument. In this case we study the following integral equation x( t) = a( t) + ( Tx)( t) integral(sigma( t))(0) u( t, s, x( s), x(lambda s)) ds 0 < lambda< 1 which can be considered in connection with the following Cauchy problem x'( t) = u( t, s, x( t), x(lambda t)), t is an element of[ 0, 1], 0 <. < 1 x( 0) = u(0).
ISSN: 1439-8516
DOI: 10.1007/s10114-007-0956-2
Source: Acta Mathematica Sinica, English Series [ISSN 1439-8516],v. 23 (9), p. 1719-1728
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