Inverse problems for Sturm–Liouville operators on a compact equilateral graph by partial nodal data

Abstract

Partial inverse nodal problems for Sturm-Liouville operators on a compact equilateral star graph are investigated in this paper. Uniqueness theorems from partial twin-dense nodal subsets in interior subintervals or arbitrary interior subintervals having the central vertex are proved. In particular, we posed and solved a new type partial inverse nodal problems for the Sturm-Liouville operator on the compact equilateral star graph.

Reconstruction of the nonlocal Sturm-Liouville operator with boundary conditions depending on the parameter

“…In 1997, Yang [35] obtained a definite algorithm for the solution of inverse nodal problems with separated boundary conditions. Later, similar results for various boundary conditions were obtained in (see [1,[4][5][6][7]10,11,[14][15][16][17][18][19]21,28,[30][31][32][36][37][38] and references therein). On the other hand, it can be said that the inverse nodal problem for nonlocal boundary conditions is a relatively new topic.…”

The Uniqueness of Sturm-Liouville Problems on a P-Star Graph

“…qx is an integrable and real-valued function on [0,1]. Recently the inverse problems for differential operators on graphs have been widely investigated [1,3,4,7,[13][14][15][16]18]. Inverse problems for Sturm-Liouville problem on quantum graphs have many applications in mathematics, chemistry, and engineering [7].…”

Inverse nodal problems for Sturm–Liouville operators on quantum star graphs

“…Hald [2][3][4]. Several works improved their methods and extended them to other problems and different boundary conditions [5][6][7][8][9][10], the quasilinear p-Laplacian operator [11,12], differential pencils [13,14], eigenvalue depending coefficients or boundary conditions [15,16], and also to quantum graphs [17][18][19][20][21][22][23]. However, most of these works assume the existence of a formula for the asymptotic behavior of eigenvalues or developed it using transmutation operators and Prufer's type transformations.…”