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2018 Solutions for second order nonlocal BVPs via the generalized Miranda theorem
Mateusz Krukowski, Katarzyna Szymańska-Debowska
Rocky Mountain J. Math. 48(2): 519-528 (2018). DOI: 10.1216/RMJ-2018-48-2-519

Abstract

In this paper, the generalized Miranda theorem is applied for second-order systems of differential equations with one boundary condition given by Riemann-Stieltjes integral \[ x'' = f(t,x,x'), \quad x(0) = 0, \ x'(1) = \int _0^1 x(s) \, dg(s),\] where $f : [0,1]\times \mathbb{R} ^k\times \mathbb{R} ^k \to \mathbb{R} ^k$ is continuous and $g : [0,1] \to \mathbb{R} ^k$ has bounded variation. Under suitable assumptions upon $f$ and $g$ we prove the existence of solutions to such posed problem.

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Mateusz Krukowski. Katarzyna Szymańska-Debowska. "Solutions for second order nonlocal BVPs via the generalized Miranda theorem." Rocky Mountain J. Math. 48 (2) 519 - 528, 2018. https://doi.org/10.1216/RMJ-2018-48-2-519

Information

Published: 2018
First available in Project Euclid: 4 June 2018

zbMATH: 06883479
MathSciNet: MR3810463
Digital Object Identifier: 10.1216/RMJ-2018-48-2-519

Subjects:
Primary: 34B10
Secondary: 34B15

Rights: Copyright © 2018 Rocky Mountain Mathematics Consortium

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Vol.48 • No. 2 • 2018
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