Research On The Problems Of Telegraph Systems And Stationary Version

Maximum principles for the linear telegraph equation and the coupled linear telegraph system have been built. They are important to the positive estimates of doubly periodic solutions. In the frame of the two principles, we will do some research on two kinds of problems: first, this thesis is concernded with the existence and multiplicity of doubly periodic solutions of a coupled nonlinear telegraph systems. And second, the existence and multiplicity of weak solutions of a stationary version. The main research topics include as follows:1. Using the fixed point theorem and the theory of index, we will study the existence and multiplicity results of doulby periodic weak solutions of the telegraph system with two parameters.2. Using the fixed point, we are concernded with the existence of doubly periodic solutions of the telegraph system with two kinds of nonlinearities: one is bounded from below, and the other is singular.3. The generalized quasilinearization techniqueis applied to obtain a monotone sequence of iterates converging uniformly and quadratically to a solution of a coupled telegraph system. In addition, Using the method of monotone iteration and Schauder fixed point theorem we establish the existence of doubly periodic solutions for a coupled nonlinear telegraph system with indefinite weight.4. Using the fixed point theorem and the mountain pass lemma, we will study the existence and multiplicity of solutions of a second order odinary differential systems and a fourth order elliptic equations...