電報方程組雙周期正解問題.pdf

1、南京航空航天大學(xué)碩士學(xué)位論文電報方程組雙周期正解問題姓名：王方磊申請學(xué)位級別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：安玉坤20080201電報方程組雙周期正解問題 ii Abstract Because of the important physical background, many people pay attention to the existence of periodic solution for the telegraph equ

2、ation and do much study work, such as the existence of double periodic solution on time and space, the existence of periodic solution on time with Dirichelet boundary condition, and the other related study. In this paper

3、, we mainly consider the existence of wealy double periodic solution for a class of coupled telegraph systems. First of all, we obtain the sufficient conditions of the existence of at least one, two, or three double peri

4、odic positive solutions for the nonlinear telegraph system using Fixed point theorem of cone mapping (Fixed theorem of cone expansion and comprehension) and topological degree approaches (Leggett-Williams multiple fixed

5、theorem). Second, we obtain a maximum principle for the linear doubly periodic telegraph system using an abstract result in a recent paper by Correa and Souto[5]. We discuss the existence of double periodic positive solu

6、tions for the nonlinear telegraph system on the basis of the above maximum using the method of upper and lower solution and thereom of fixed point index. Finally, we study two telegraph systems with more general nonlinea

7、r terms. One is that the nonlinear term may be negative, we call such problem as semipositone problem, so we discuss the existence of double periodic positive solution for the semipositone telegraph system. Another is th

8、at the nonlinear term may be singular, we also consider the existence of double periodic positive solution of the singular telegraph system. Keywords: telegraph system, maximum principle, doubly periodic solutions, cone,