Existence of Nondecreasing and Continuous Solutions of an Integral Equation with Linear Modification of the Argument |
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Authors: | J CABALLERO B LÓPEZ K SADARANGANI |
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Institution: | (1) Departamento de Matemáticas, Universidad de Las Palmas de Gran Canaria, Campus de Tafira Baja, 35017 Las Palmas de Gran Canaria, Spain |
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Abstract: | We use a technique associated with measures of noncompactness to prove the existence of nondecreasing solutions to an integral
equation with linear modification of the argument in the space C0, 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 modifications of the argument. In this case we study the
following integral equation
which can be considered in connection with the following Cauchy problem x'(t) = u(t, s, x(t), x(λt)), t ∈ 0, 1], 0 < λ < 1 x(0) = u
0.
Supported partially by the "Consejería de Educación, Cultura y Deporte del Gobierno de Canarias" P.I. 2003/068 and by "Ministerio
de Educación y Ciencia" MTM2004/05878 |
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Keywords: | measure of noncompactness fixed point theorem nondecreasing solutions |
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