Half-inverse problems for differential operators

This thesis consist of four chapters.In the first chapter the history of spectral theory a Sturm-Liouville and Dirac operators were given.In the second chapter some fundamental definitions, often used in spectral theory of differential operators, were given.In the third chapter half-Inverse problems on the finite interval for Sturm-Liouville equation were given.In the fourth chapter original works have been done. In this chapter, isospectrality problem for Classical Sturm-Liouville equation were given and isospectrality problem were researched for Dirac systems.Key Words: Sturm-Liouville Equation, Half-Inverse Problem, Gelfand-Levitan Integral Equation, Transmutation Operator, Isospectrality Problem, Dirac Systems.