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2019 Some two-point problems for second order integro-differential equations with argument deviations
Sulkhan Mukhigulashvili, Veronika Novotná
Topol. Methods Nonlinear Anal. 54(2A): 459-476 (2019). DOI: 10.12775/TMNA.2019.045

Abstract

In the paper we describe the classes of unique solvability of the Dirichlet and mixed two point boundary value problems for the second order linear integro-differential equation $$ u''(t)=p_0(t)u(t)+p_1(t)u(\tau_1(t))+\int_{a}^{b}p(t,s)u(\tau(s))\,ds+ q(t). $$ On the basis of the obtained and, in some sense, optimal results for the linear problems, by the a priori boundedness principle we prove the theorems of solvability and unique solvability for the second order nonlinear functional differential equations under the mentioned boundary conditions.

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Sulkhan Mukhigulashvili. Veronika Novotná. "Some two-point problems for second order integro-differential equations with argument deviations." Topol. Methods Nonlinear Anal. 54 (2A) 459 - 476, 2019. https://doi.org/10.12775/TMNA.2019.045

Information

Published: 2019
First available in Project Euclid: 21 October 2019

zbMATH: 07198792
MathSciNet: MR4061305
Digital Object Identifier: 10.12775/TMNA.2019.045

Rights: Copyright © 2019 Juliusz P. Schauder Centre for Nonlinear Studies

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Vol.54 • No. 2A • 2019
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