Periodic solutions of nonlinear ordinary differential equations

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Kalenge, Mathias Chifuba
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Many physical problems are studied through mathematical equations especially differential equations. For example, problems in mechanics, electricity, aerodynamics, to mention just a few, use differential equations. While it is true to say that physical sciences and tech¬nology are the two main sources of problems which require the use of differential equations, biological and social sciences are increas¬ingly being realised as other sources. For example population study is one area where differential equations are applied. Much of the literature on differential equations is on linear differential equations. Methods of solving a variety of linear differential equations are known but most of these methods cannot * * be effectively extended to nonlinear differential equations. This makes the solving of nonlinear equations a difficult task. What has been done to ease this problem is to abandon the idea of solving an equation and instead get as much information as is possible about a class of solutions of the nonlinear differential equation by examining the equation itself. After extracting enough information, then one can find ways of approximating a particular solution as the exact one is almost impossible to get. This work is a brief- survey of the literature available concern¬ing periodic solutions of nonlinear ordinary differential equations. Chapter 1 is on the standard existence theory of differential equations. Chapter 2 is a brief account of critical points and Chapter 3 is on stability theory. The last chapter looks at some of the existence theorems for periodic solutions of nonlinear differential equations. References are given at the end.
Differential equations , Differential algebra. , Equations. , Differential equations, Nonlinear.