Department of Mathematics
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Item Asymptotic Methods for some third order Nonlinear Differential Equations(University of Rajshahi, 1995) Alam, Md. Shamsul; Sattar, Muhammad AbdusIn this thesis, we investigate the oscillations of third order nonlinear systems by the asymptotic method. The asymptotic method of Krylov-Bogoliubov-Mitropolskii (KBM) is a popular technigue for obtaining analytic solution of a second order nonlinear oscillatory system. First a third order nonlinear differential system modeling nonoscillatory process and characterized by critical damping is considered and a new perturbation technigue is developed, based on the work of Krylov-Bogoliubov-Mitropolskii, to £ind the solution of the system. Then a method is presented unifying both third order damped and overdamped systems. This method is a generalization of Bogoliubov·s asymptotic method and covers all the cases when the roots of the corresponding linear equation are real, real and complex, and real and purely imaginary.Later a third order forced nonlinear differential system modeling oscillatory process is considered and a new perturbation technique is developed to find the solution of the system. The methods are illustrated by several examples.