Related papers: Unique solvability of a coupling problem for entir…
For finite dimensional CMV matrices the classical inverse spectral problems are considered. We solve the inverse problem of reconstructing a CMV matrix by its Weyl's function, the problem of reconstructing the matrix by two spectra of CMV…
This article deals with the second order linear differential equations with entire coefficients. We prove some results involving conditions on coefficients so that the order of growth of every non-trivial solution is infinite.
In this paper the asymptotic distributions are exactly solved for linearly independent solutions considering problems of the second order and for the coefficients of asymptotic destribution the recurent formulas are obtained. Further, using…
The emergence of conformal states is established for any problem involving a domain of scales where the long-range, SO(2,1) conformally invariant interaction is applicable. Whenever a clear-cut separation of ultraviolet and infrared cutoffs…
This research was devoted to investigate the inverse spectral problem of Sturm-Liouville operator with many frozen arguments. Under some assumptions, the authors obtained uniqueness theorems. At the end, a numerical simulation for the…
Nonlinear second-order ordinary differential equations are common in various fields of science, such as physics, mechanics and biology. Here we provide a new family of integrable second-order ordinary differential equations by considering…
The inverse problem for the Sturm- Liouville operator with complex periodic potential and positive discontinuous coefficients on the axis is studied. Main characteristics of the fundamental solutions are investigated, the spectrum of the…
As a continuation of our previous work \cite{KV2} the aim of the recent paper is to investigate the solutions of special inhomogeneous linear functional equations by using spectral synthesis in translation invariant closed linear subspaces…
For a given self-adjoint operator $A$ with discrete spectrum, we completely characterize possible eigenvalues of its rank-one perturbations~$B$ and discuss the inverse problem of reconstructing $B$ from its spectrum.
We discuss the occurrence of oscillatory solutions which decay to 0 as $s\to+\infty$ for a class of perturbed second order ordinary differential equations. As opposed to other results in the recent literature, the perturbation is as small…
We study entire functions whose zeros and one-points lie on distinct finite systems of rays. General restrictions on these rays are obtained. Non-trivial examples of entire functions with zeros and one-points on different rays are…
We prove some uniqueness results for weak solutions to some classes of parabolic Dirichlet problems.
The existence of anomalous symmetry-breaking solutions of the SO(2,1) commutator algebra is explicitly extended beyond the case of scale-invariant contact interactions. In particular, the failure of the conservation laws of the dilation and…
Populations of phase oscillators interacting globally through a general coupling function $f(x)$ have been considered. In the absence of precessing frequencies and for odd-coupling functions there exists a Lyapunov functional and the…
We study some natural sets arising in the theory of ordinary differential equations in one variable from the point of view of descriptive set theory and in particular classify them within the Borel hierarchy. We prove that the set of Cauchy…
This \textquoteleft research-survey' is meant for beginners in the studies of integrable systems. Here we outline some analytical methods for dealing with a class of nonlinear partial differential equations. We pay special attention to…
Recently developed supersymmetric perturbation theory has been successfully employed to make a complete mathematical analysis the reason behind exact solvability of some non-central potentials. This investigation clarifies once more the…
In this paper, we employ the theory of normal families in several complex variables to obtain some uniqueness theorems for entire functions. These results extend the related works of Li and Yi [11], and Lu et al. [18] to the setting of…
We prove that solutions to elliptic equations in two variables in divergence form, possibly non-selfadjoint and with lower order terms, satisfy the strong unique continuation property.
We prove an existence and uniqueness theorem for exact WKB solutions of general singularly perturbed linear second-order ODEs in the complex domain. These include the one-dimensional time-independent complex Schr\"odinger equation. Notably,…