Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Asymptotic behaviour and oscillation of classes of integrodifferential equations
HTML articles powered by AMS MathViewer

by A. H. Nasr PDF
Proc. Amer. Math. Soc. 116 (1992), 143-148 Request permission

Abstract:

Under some conditions on the integrodifferential equations \[ \ddot y\left ( t \right ) + \int _0^t {k\left ( {t - s} \right )y\left ( s \right )ds + \varphi \left ( t \right )} \int _0^t {K\left ( {t - s} \right )\dot y\left ( s \right )ds = f\left [ {t,y\left ( t \right ),\dot y\left ( t \right ),\int _0^t {g\left ( {t,s,y\left ( s \right ),\dot y\left ( s \right )} \right )ds} } \right ]} ,\quad t \geq 0,\], \[ \ddot y\left ( t \right ) + \int _1^t {k\left ( {\frac {t}{s}} \right )y\left ( s \right )} \frac {1}{s}ds + \varphi \left ( t \right )\int _1^t {K\left ( {\frac {t}{s}} \right )\dot y\left ( s \right )ds = f\left [ {t,y\left ( t \right ),\dot y\left ( t \right ),\int _1^t {g\left ( {t,s,y\left ( s \right ),\dot y\left ( s \right )} \right )ds} } \right ],\quad t \geq 1,} \], the explicit asymptote of solutions is proved to be $y\left ( t \right ) = A\sin \left ( {\omega t + \delta } \right )$ as $t \to \infty$. From this asymptote, the oscillatory behavior of the equations, the limit of the amplitudes, and the limit of the distance between consecutive zeros of the solutions are evident. Their definite values are also determined.
References
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC: 34K15, 34K25, 45J05
  • Retrieve articles in all journals with MSC: 34K15, 34K25, 45J05
Additional Information
  • © Copyright 1992 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 116 (1992), 143-148
  • MSC: Primary 34K15; Secondary 34K25, 45J05
  • DOI: https://doi.org/10.1090/S0002-9939-1992-1094505-6
  • MathSciNet review: 1094505