Investigation of the stability of solutions of some direct and inverse problems for ultrahyperbolic schrödinger equations

This thesis consists of six chapters. The first chapter is devoted to the main results on the direct and inverse problems for classical and ultrahyberbolic Schrödinger equations in the literature. In the second chapter, some basic definitions and theorems that are used to investigate the solvability of these problems are presented. In the third chapter, some of the major results in the literature on the existence and uniqueness of the solution of Cauchy problem for partial differential equations are discussed. In the fourth chapter, various examples of the applications of inverse and ill-posed problems in science and technology are given. In the fifth chapter, a local Carleman estimate for the ultrahyperbolic Schrödinger equation is obtained and the Hölder stability for the Cauchy Problem is proved. In the last chapter, we obtain a global Carleman estimate and prove conditional Hölder stability for some inverse problems for the ultrahyperbolic Schrödinger equation.