In this paper, for the first time, we study inverse Sturm–Liouville problem with polynomials of spectral parameter in boundary condition and entire analytic functions second one. For investigation new problem, develop an approach based on construction a special vector functional sequence suitable Hilbert space. The uniqueness recovering potential from part spectrum is proved. Furthermore, our m...

This paper is concerned with a study of special integral equation. equation arises in many applied problems, including transmutation theory, inverse scattering the solution singular Sturm–Liouville and Shrödinger equations, representation solutions equations. A derived formulated using Riemann function hyperbolic In paper, existence unique to this proven by method successive approximations. The...

This paper deals with the problem of determining the leading coefficient k 1⁄4 kððu0ÞÞ of the nonlinear (monotone potential) Sturm–Liouville operator Au1⁄4 ðkððu0ÞÞu0ðxÞÞþ qðxÞuðxÞ, x2 ða;bÞ. As an additional condition only two measured data at the boundary (x1⁄4 a, x1⁄4 b) are used. Solvability and linearization of the corresponding nonlinear direct problem are given. An existence of a quasi-s...

Abstract In this paper, the heat conduction equation for composite materials posed and solved. The inverse Boundary Value Problem (BVP) described By studying solving direct problem in materials, we can determine function spaces solve problem. Sturm-Liouville method was used to by reduce it integral first kind. value be formulated as an kind equations. discretization algorithm applied reformulat...

This paper deals with the boundary value problem involving the differential equation ell y:=-y''+qy=lambda y, subject to the eigenparameter dependent boundary conditions along with the following discontinuity conditions y(d+0)=a y(d-0), y'(d+0)=ay'(d-0)+b y(d-0). In this problem q(x), d, a , b are real, qin L^2(0,pi), din(0,pi) and lambda is a parameter independent of x. By defining a new...

The operator of double differentiation, perturbed by the composition differentiation and a convolution one, on finite interval with Dirichlet boundary conditions is considered. We obtain uniform stability recovering kernel from spectrum in weighted $L_2$-norm norm. For this purpose, we successively prove each step algorithm for solving inverse problem both norms. Besides justifying numerical co...

In this study we consider the Kaup–Boussinesq system with a self-consistent source. We show that source can be integrated by method of inverse scattering theory. For solving problem under consideration, use direct and Sturm–Liouville equation an energy-dependent potential. The time evolution data for potentials associated solution is determined. obtained equalities completely determine any $t$,...