Transmutations, Singular and Fractional Differential Equations with Applications to
Mathematical Physics connects difficult problems with similar more simple ones. The book's …

This book provides an introduction to the most recent developments in the theory and
practice of direct and inverse Sturm-Liouville problems on finite and infinite intervals. A …

Based on the second derivative, this paper directly establishes the coincidence degree
theory of a nonlinear periodic Sturm–Liouville (SL) system. As applications, we study the …

This textbook provides a thorough overview of mathematical physics, highlighting classical
topics as well as recent developments. Readers will be introduced to a variety of methods …

The inverse quantum scattering problem for the perturbed Bessel equation is considered. A
direct and practical method for solving the problem is proposed. It allows one to reduce the …

This is a brief overview of some recent developments in the transmutation operator
approach to practical solution of mathematical physics problems. It introduces basic notions …

A method for solving inverse quantum scattering problems on a half line is proposed. It is
based on the application of the transmutation operators and recent results on series …

In this paper, an approach to solving direct and inverse scattering problems on the half-line
for a one-dimensional Schrödinger equation with a complex-valued potential that is …

New representations for an integral kernel of the transmutation operator and for a regular
solution of the perturbed Bessel equation of the form− u ″+ ℓ (ℓ+ 1) x 2+ q (x) u= ω 2 u are …

The inverse problem of the reconstruction of the Sturm–Liouville problem on a half-line from
its Weyl function is considered. Given the Weyl function, we obtain the potential in the …