In recent years, there appeared a growing interest in the inverse spectral theory for functional-differential operators with frozen argument. Such are nonlocal and belong to so-called loaded differential operators, which frequently appear mathematics as well natural sciences engineering. However, various classes of classical methods not applicable. For this reason, it is relevant develop new ap...

We give a systematic account of isospectral deformations for Sturm-Liouville and Dirac-type operators and associated hierarchies of nonlinear evolution equations. In particular, we study generalized KdV and modified KdV-hierarchies and their reduction to the standard (m)KdV-hierarchy. As an example we study the Harry Dym equation in some detail and relate its solutions to KdV-solutions and to H...

We provide a complete spectral characterization of the double commutation method for general Sturm-Liouville operators which inserts any finite number of prescribed eigenvalues into spectral gaps of a given background operator. Moreover, we explicitly determine the transformation operator which links the background operator to its doubly commuted version (resulting in extensions and considerabl...

In this work we study the different type of regular boundary value problems on a path associated with the Schrödinger operator. In particular, we obtain the Green function for each problem and we emphasize the case of Sturm-Liouville boundary conditions. In any case, the Green function is given in terms of second kind Chebyshev polynomials since they verify a recurrence law similar to the one v...

As we know one of the most important equations which have many applications in various areas physics, mathematics, and financial markets, is Sturm–Liouville equation. In this paper, by using α-ψ-contraction technique fixed point theory employing some functional inequalities, study existence solutions partial fractional hybrid case generalized Sturm–Liouville-Langevin under boundary value condit...

In this manuscript, we consider the inverse problem for non self-adjoint Sturm--Liouville operator $-D^2+q$ with eigenparameter dependent boundary and discontinuity conditions inside a finite closed interval. We prove by defining a new Hilbert space and using spectral data of a kind, the potential function can be uniquely determined by a set of value of eigenfunctions at an interior point and p...

We prove a necessary optimality condition for isoperimetric problems on time scales in the space of delta-differentiable functions with rdcontinuous derivatives. The results are then applied to Sturm-Liouville eigenvalue problems on time scales.

In the present paper, the Liouville theorem and the finite dimension theorem of polynomial growth harmonic functions are proved on Alexandrov spaces with nonnegative Ricci curvature in the sense of Sturm, Lott-Villani and Kuwae-Shioya.

This paper [1] has been retracted as it is essentially identical in content with the published article " Determination of Sturm-Liouville operator on a three-star graph from four spectra, " by Dehghani Tazehkand and Akbarfam, published in Acta