| Before Newton and Leibniz set up the system of calculus, many people have already studied the differential equation in physics. One of the most famous example is that when Galileo were studying the freefall motion, he found a differential equation as x"=g, and got its solution as this formula is so famous and all we call it the freefall motion formula. Of course it is famous because it is the first differential equation as we know.After the building of the theory system of calculus, many methods were used for researching the differential equation and got millions of results. One of most important is the periodic solution of differential equation. When studied the periodic solution,, many people found that many equations have special solutions that never noticed, it is the anti-periodic solution. So from1980s, many mathematicians started to research the anti-periodic solution. For studying the anti-periodic solution, many tools were used, for example, the theory of Leray-Schauder degree, Leray-Schauder fixed point theory and Fourier analysis methods, the coupled upper-lower solution and monotone iteration methods, topology degree theory and upper and lower solution theory, and so on.This dissertation studies two differential equation systems:The anti-periodic-solution of p-Laplacian neutral differential function with variable parameters, the anti-periodic solution of p-Laplacian neutral differential function with variable parameters, the two classes equations have already been studied by many people. This dissertation study the equations by using the methods of Leray-Schauder fixed point theory and achieve the confidence condition of the existence of the solution. In the first part of this dissertation, we introduce the history of the anti-periodic solution and some results in and out of county recently.In the second part of this dissertation, we study the anti-periodic solution of p-Laplacianneutral differential function with variable parameters, and give the proof about the main conclusion.In the third part of the dissertation, we study the anti-periodic solution of p-Laplacian neutral differential function with variable parameters, and prove the conclusion.In the last part, we conclude the study and give some problems that should be study in the future. |
