In this manuscript, we study 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. By defining  a new Hilbert space and  using its spectral data of a kind, it is shown that the potential function can be uniquely determined by part of a set of values of eigenfunctions at som...

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...

In this paper, in an arbitrary Hilbert space nonlocal boundary value problem for the Schrödinger equation with time dependent self-adjoint operator is studied. Stability estimates solution of established. To find approximate first order accuracy Rothe difference scheme and second Crank-Nicholson are constructed. these schemes have been obtained. obtain stability estimates, theory spectral repre...

Linear boundary value problems in heat conduction have been investigated extensively for a diverse variety of boundary conditions, but almost invariably these have been of the type that produce self-adjoint problems. The property of selfadjointness makes it possible to obtain readily the solution of steady and unsteady-state heat conduction problems in the form of a series expansion of orthogon...

In this paper, we present a mathematically rigorous quantum-mechanical treatment of a one-dimensional motion of a particle in the Calogero potential αx−2 . Although the problem is quite old and well-studied, we believe that our consideration, based on a uniform approach to constructing a correct quantum-mechanical description for systems with singular potentials and/or boundaries, proposed in o...

In this work we consider the problem on group classification and conservation laws of general first order evolution equations. We obtain subclasses these equations which are quasi-self-adjoint self-adjoint. By using recent Ibragimov's Theorem laws, establish admiting self-adjoint illustrate our results applying them to inviscid Burgers' equation. particular an infinite number new symmetries fou...