Eigenvalues in the essential spectrum of a weighted Sturm-Liouville operator are studied under the assumption that the weight function has one turning point. An abstract approach to the problem is given via a functional model for indefinite Sturm-Liouville operators. Algebraic multiplicities of eigenvalues are obtained. Also, operators with finite singular critical points are considered. MSC-cl...

We study conformal mappings from the unit disk to circular-arc quadrilaterals with four right angles. The problem is reduced to a Sturm-Liouville boundary value problem on a real interval, with a nonlinear boundary condition, in which the coefficient functions contain the accessory parameters t, λ of the mapping problem. The parameter λ is designed in such a way that for fixed t, it plays the r...

We construct multiplicative Green?s (or +Green?s) function for *Sturm-Liouville (*SL) equation. The basic properties of *Green?s are given. Then, *SL equation is evaluated by using function. Effectiveness in *case will thus be seen some examples.

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...

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 solve the inverse spectral problem for a class of Sturm–Liouville operators with singular nonlocal potentials and nonlocal boundary conditions.

The general properties of a class of two-dimensional dilaton gravity (DG) theories with multiexponential potentials are studied and a subclass of these theories, in which the equations of motion reduce to Toda and Liouville equations, is treated in detail. A combination of parameters of the equations should satisfy a certain constraint that is identified and solved for the general multi-exponen...