Stability Theory Of Differential Equations

Suitable for advanced undergraduates and graduate students this was the first Englishlanguage text to offer detailed coverage of boundedness stability and asymptotic behavior of linear and nonlinear differential equations. It remains a classic guide featuring material from original research papers including the authors own studies. The linear equation with constant and almostconstant coefficients receives indepth attention that includes aspects of matrix theory. No previous acquaintance with the theory is necessary since author Richard Bellman derives the results in matrix theory from the beginning. In regard to the stability of nonlinear systems results of the linear theory are used to drive the results of Poincaré and Liapounoff. Professor Bellman then surveys important results concerning the boundedness stability and asymptotic behavior of secondorder linear differential equations. The final chapters explore significant nonlinear differential equations whose solutions may be completely described in terms of asymptotic behavior. Only real solutions of real equations are considered and the treatment emphasizes the behavior of these solutions as the independent variable increases without limit.