Inverse nodal problem for diffusion operator

This thesis is arranged in three chapters. In the first chapter, some concepts used in this thesis are given and general properties of generalized sine function, some theorems and lemmas that are concerning this function were given. Then, Prüfer substitution for one dimensional p-Laplacian equation is defined and some properties of this substitution are explained. In the second chapter, inverse nodal problem for p-Laplacian diffusion operator is solved with Dirichlet boundary conditions. And a Prüfer substitution for this operator is defined. Furthermore, Asymptotic formulas for eigenvalues and nodal parameters are obtained by using this substitution. Finally, a reconstruction formula for q potential function is given. In the third chapter, Lipschitz stability of diffusion operator is studied by using a homeomorphism between two metric spaces