Electron. J. Differential Equations, Vol. 2017 (2017), No. 262, pp. 1-12.

Existence of solutions to a boundary-value problem for an infinite system of differential equations

Jozef Banas, Mohammad Mursaleen, Syed M. H. Rizvi

Abstract:
Using techniques associated with measures of noncompactness we prove an existence of solutions for a boundary-value problem for an infinite system of ordinary differential equations of second order. Our approach depends on transforming of the original boundary-value problem into an infinite system of integral equations of Fredholm type. The settings for this article are in the classical Banach sequence space $l_p$ with $p\geq 1$.

Submitted August 3, 2017. Published October 17, 2017.
Math Subject Classifications: 34G20, 47H08.
Key Words: Measure of noncompactness; equicontinuous family; boundary value problem; infinite system of differential equations; Fredholm integral equation.

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Jozef Banas
Department of Nonlinear Analysis
Rzeszow University of Technology
al. Powstancow Warszawy 8, 35-959 Rzeszow, Poland
email: jbanas@prz.edu.pl
Mohammad Mursaleen
Department of Mathematics
Aligarh Muslim University
Aligarh 202002, India
email: mursaleenm@gmail.com
Syed M. H. Rizvi
Department of Mathematics
Aligarh Muslim University
Aligarh 202002, India
email: syedrizvi022@gmail.com

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