On some inverse problems as to nodal points of sturm-liouville operators

ABSTRACTMasters ThesısON SOME INVERSE PROBLEMS AS TO NODAL PO NTS OFSTURM-LIOUVILLE OPERATORSNeslihan CEYLANFırat UniversityGraduate School of Science and TechnologyDepartment of Mathematics2006, Page:69This study is arranged in five chapters.In the first chapter; Some fundamental definitions and theorems that use often inSpectral theory of Differential operators are given.In the second chapter; General informations of Sturm-Liouville operators, regularand singular Sturm-Liouville operators, asymptotic formulas for the eigenvalues andeigenfunctions, zeros of eigenfunctions and oscıllatıon theorem are examined.In the third chapter; Inverse nodal problem and vectorial inverse nodal problemare given.In the fourth chapter; The inverse nodal problem due to Yang is examined andproof of main theorem is given.In the fifth chapter;Dirichlet and other boundary conditions of vectorial Sturm-Liouville equation are examined. Seperately ,inverse spectral theory using nodal pointsas data a uniqueness result is examined.Keywords: Sturm-Liouville Operators, eigenvalues , eigenfunctions, nodal points,oscıllatıon theorem, inverse nodal problem, spectrum, dirichlet conditions,regular andsingular operators