Journal of Mathematical Sciences

, Volume 230, Issue 5, pp 688–694 | Cite as

On Lower Estimates of Solutions and Their Derivatives to a Fourth-Order Linear Integrodifferential Volterra Equation

Article

Abstract

We examine solutions of the problem on sufficient conditions that guarantee a lower estimate and tending to infinity of solutions and their derivatives up to the third order to a fourth-order linear integrodifferential Volterra equation. For this purpose, we develop a method based on the nonstandard reduction method (S. Iskandarov), the Volterra transformation method, the method of shearing functions (S. Iskandarov), the method of integral inequalities (Yu. A. Ved’ and Z. Pakhyrov), the method of a priori estimates (N. V. Azbelev, V. P. Maksimov, L. F. Rakhmatullina, and P. M. Simonov, 1991, 2001), the Lagrange method for integral representations of solutions to first-order linear inhomogeneous differential equations, and the method of lower estimate of solutions (Yu. A. Ved’ and L. N. Kitaeva).

Keywords and phrases

integrodifferential equation a priori estimate lower estimate initial data instability 

AMS Subject Classification

53A40 2015 

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute of Theoretical and Applied Mathematics of the National Academy of Sciences of the Kyrgyz RepublicBishkekKyrgyzstan
  2. 2.Kyrgyz-Russian Academy of EducationBishkekKyrgyzstan

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