INVERSE NODAL PROBLEM FOR p LAPLACIAN DIFFUSION EQUATION WITH POLYNOMIALLY DEPENDENT SPECTRAL PARAMETER TUBA GULSEN AND EMRAH YILMAZAbstract. In this study, solution of inverse nodal problem for one-dimensional p-Laplacian di¤usion equation is extended to the case that boundary condition depends on polynomial eigenparameter. To …nd the spectral datas as eigenvalues and nodal parameters of this problem, we used a modi…ed Prüfer substitution. Then, reconstruction formula of the potential function is also given by using nodal lenghts. Furthermore, this method is similar to used in [1], our results are more general.(Dedicated to Prof. E. S. Panakhov on his 60-th birthday)

Abstract. In this study, we are enunciative of some asymptotic expansions and reconstruction formulas for inverse nodal problem of p-Laplacian Bessel equation. Furthermore, Lipschitz stability problem for this equation with Dirichlet boundary conditions is solved. And, it is also proved that the space of all potential functions w is homeomorphic to the partition set of all asymptotically equivalent nodal sequences induced by an equivalence relation.