SOME RESULTS IN THE EXISTENCE, UNIQUENESS AND STABILITY PERIODIC SOLUTION OF NEW VOLTERRA INTEGRAL EQUATIONS WITH SINGULAR KERNEL
(1) Department of Mathematics, Collage of Basic Education, University of Duhok.
The aim of this work is to study the existence, uniqueness and stability of periodic solutions of some classes for non-linear systems of new Volterra integral equations with singular kernel in two variables by using Riemann integrals. Furthermore, we investigation the existence, uniqueness and stability of the fundamental tools employed in the analysis are based on applications by depending on the numerical-analytic method for studying the periodic solutions of ordinary differential equations which were introduced by Samoilenko.The study of such nonlinear Volterra integral equations with singular kernel leads us to improve and extend Samoilenko method. Thus the non-linear integral equations with singular kernel that we have introduced in the study become more general and detailed than those introduced by Butris .
. Butris, R. N., Solution for the Volterra Integral Equations of Second kind, M. Sc.Thesis, Mosul University, Iraq (1984).
.Faris, B., S., Periodic solutions for some classes of nonlinear systems of integral equations of M. Sc. Thesis, University of Zakho, (2013).
. Korol I.’ and. Perestyuk, M. O. Once Again on The Samoilenko Numerical-Analytic Method of Successive Periodic Approximations, Ukrainian Mathematical Journal, Vol. 58, No. 4,( 2006).
. Luchka, A. Yu. New Approach to the Investigation of the Existence of Periodic Solutions of Systems of Differential Equations and their Construction, Nonlinear Oscillations, Vol. 11, No. 1,( 2008).
. Mitropolsky Yu. A. and Martynyuk D. I., For Periodic Solutions for the Oscillations Systems with Retarded Argument, Kiev, Ukraine (1979).
. Parton, V. Z. and Perlin, P. I., Integral Equations in Elasticity, Mir Publishers, Moscow(1982),
. Ronto, M. On Two Numerical-Analytic Methods for the Investigation of Periodic Solutions, Periodica Mathematica Hungarica Vol. 56 (1 ), (2008).
. Rontó, A. Rontó, M. Holubová G. and Nečesal, P. Numerical-analytic technique for investigation of solutions of some nonlinear equations with Dirichlet conditions, licensee Springer.( 2011).
. Samoilenko A. M. and Ronto N. I., A numerical-analytic method for investigations of Periodic Solutions, Kiev, Ukraine (1976).
. Samoilenko, A. M. Numerical-analytic method for the investigation of periodic systems of ordinary differential equations. 1,Ukr. Mat. Zh., 17, No. 4, (1965).
. Struble, R. A., Non-Linear Differential Equations, Mc Graw- Hall Book Company Inc., New York (1962).
. Shestopalov, Y. V. and Smirnov, Y. G., Integral Equations, Karlstad University. (2002).
. Tarang, M., Stability of the spline collocation method for Volterra integro-differential equations, Thesis, University of Tartu, (2004).
. Tricomi, F. G., Integral Equations, Turin University, Turin,Italy, June. (1965).
Article MetricsAbstract View : 79 times
PDF Download : 17 times
- There are currently no refbacks.