In this work, we study the following conformable fractional Sturm--Liouville
 problem
 \[
 l[y]=-T_{\alpha }(p(t)T_{\alpha }y(t))+q(t)y(t),
 \]
 where $t\in \lbrack 0,\infty ),$ real-valued functions $p$ and $q$
 satisfy conditions:
 \begin{array}{cc}
 (i) & q\in L_{\alpha }^{2}[0,\infty ), \\ 
 (ii) p\ \text{is\ absolutely\ continuous\ on}\ [0,\...

Recently, there appeared a considerable interest in inverse Sturm–Liouville-type problems with constant delay. However, necessary and sufficient conditions for solvability of such were obtained only one very particular situation. Here we address this gap by obtaining the case functional-differential pencils possessing more general form along nonlinear dependence on spectral parameter. For purpo...

We give an example of an indefinite weight Sturm-Liouville problem whose eigenfunctions form a Riesz basis under Dirichlet boundary conditions but not under anti-periodic boundary conditions.

We consider finite difference approximations of solutions of inverse Sturm-Liouville problems in bounded intervals. Using three-point finite difference schemes, we discretize the equations on so-called optimal grids constructed as follows: For a staggered grid with 2k points, we ask that the finite difference operator (a k ×k Jacobi matrix) and the Sturm-Liouville differential operator share th...

In this paper, we construct the new integral representation of Jost solution Sturm-Liouville equation with impuls in semi axis $[0,+\infty )$ and give type relation, examine properties Kernel function their partial derivatives $x$ $\ t$, constructed obtain differential provided by function. Finally, paper prove uniqueness determination potential scattering data.

We consider the nonlinear Sturm-Liouville problem −u′′(t) + f(u(t), u′(t)) = λu(t), u(t) > 0, t ∈ I := (−1/2, 1/2), u(±1/2) = 0, where f(x, y) = |x|p−1x − |y|m, p > 1, 1 ≤ m < 2 are constants and λ > 0 is an eigenvalue parameter. To understand well the global structure of the bifurcation branch of positive solutions in R+ ×Lq(I) (1 ≤ q < ∞) from a viewpoint of inverse problems, we establish the...

Keywords: Inverse coefficient problem (ICP) Lie-group adaptive method (LGAM) Leading coefficient Inverse Sturm–Liouville operator Iterative method a b s t r a c t We consider an inverse problem for identifying a leading coefficient a(x) in À(a(x)y 0 (x)) 0 + q(x)y(x) = H(x), which is known as an inverse coefficient problem for the Sturm–Liouville operator. We transform y(x) to u(x, t) = (1 + t)...

The main goal of this paper is to propose an approach inverse spectral problems for functional-differential operators (FDO) with involution. For definiteness, we focus on the second-order FDO involution-reflection. Our based reduction problem matrix form and solution Sturm-Liouville operator by developing method mappings. obtained contains weight, which causes qualitative difficulties in study ...