in this paper, the asymptotic representation of the corresponding eigenfunctions of the eigenvalues has been investigated. furthermore, we obtain the zeros of eigenfunctions.

In this study, inverse nodal problem is solved for the p-Laplacian operator with two potential functions. We present some asymptotic formulas which have been proved in [17,18] for the eigenvalues, nodal points and nodal lengths, provided that a potential function is unknown. Then, using the nodal points we reconstruct the potential function and its derivatives. We also introduce a solution of i...

In this paper, an inverse nodal problem for a second-order differential equation having a chemical potential on a finite interval is investigated. First, we estimate the nodal points and nodal lengths of differential operator. Then, we show that the potential can be uniquely determined by a dense set of nodes of the eigenfunctions.

An inverse nodal problem has first been studied for the Sturm-Liouville equation with one turning point. The asymptotic representation of the corresponding eigenfunctions of the eigenvalues has been investigated and an asymptotic of the nodal points is obtained. For this problem, we give a reconstruction formula for the potential function. Furthermore, numerical examples have been established a...

Consider the vectorial Sturm-Liouville problem:   −y′′(x) + P (x)y(x) = λIdy(x) Ay(0) + Idy ′(0) = 0 By(1) + Idy ′(1) = 0 where P (x) = [pij(x)]i,j=1 is a continuous symmetric matrix-valued function defined on [0, 1], and A and B are d×d real symmetric matrices. An eigenfunction y(x) of the above problem is said to be of type (CZ) if any isolated zero of its component is a nodal point of y(x...