A Class Of Fourth-order Differential Equations Of The Periodic Solution And Its Applications

An outstanding meaningful fourth order ordinary differential equation is considered, whose solutions constitute some particular solutions of a great number of partial differential equations which depend on a time and space variables. Such as stationary solutions, travelling waves and certain more solutions with complex relation between time and space variables. Therefore, it is extremely important to analyze this kind of equation generally for a great number of physical partial differential equation.The paper is arranged as follows. In chapter 1, the needed basic knowledge and some better results of certain f(t) are introduced. Next, some new and general results, obtained by the author using topological shooting method, are listed and proved in detail in chapter 2 and 3. To make it exactly, in chapter 2 that single-humped periodic solutions under what conditions can be held is considered, furthermore, an estimation of the period is given if exists. In chapter 3 the existence of multi-humped periodic solutions is considered.