Existing of solution to the higher order linear hyperbolic differential equations with variable coefficient

In the first chapter of this thesis some explanatory information on the thesis topic was given. In the second chapter, related literature was given. In the third chapter, basic definitions, theorems, equalities and inequalities that will be used throughout the thesis are given. Moreover, some theorems on solutions of second order linear hyperbolic differential equations and the solution of vibrating string problem by Fourier series method were given. The fourth chapter is the original part of this thesis and consists of two subsections. In the first part, well-posedness of solutions of higher order linear hyperbolic differential equations with variable coefficient is studied. In the second part, the solution of this problem was given by the form of Fourier series In the fifth chapter, the obtained results are summarized and suggestions are presented.