In this paper, we study the second-order nonlinear singular Sturm-Liouville boundary value problems with Riemann-Stieltjes integral boundary conditions    −(p(t)u(t)) + q(t)u(t) = f(t, u(t)), 0 < t < 1, α1u(0)− β1u (0) = ∫ 1 0 u(τ)dα(τ), α2u(1) + β2u (1) = ∫ 1 0 u(τ)dβ(τ), where f(t, u) is allowed to be singular at t = 0, 1 and u = 0. Some new results for the existence of positive solu...

We study Sturm–Liouville differential operators on the time scales consisting of finitely many isolated points and closed intervals. In author’s previous paper, it was established that such are uniquely determined by spectral characteristics all classical types. present an algorithm for their recovery based method mappings is obtained. also prove eigenvalues two boundary-value problems with one...

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...

For a system of coupled Schrödinger equations, the relationship is found between the vector-valued norming constants and M + 1 spectra of the M-channel Sturm-Liouville operator with the same potential matrix but different boundary conditions. Under a special choice of particular boundary conditions, this equation for norming vectors has a unique solution. The norming vectors derived from M + 1 ...

We extend the idea of Jodeit and Levitan [3] for constructing isospectral problems of the classical scalar Sturm-Liouville differential equations to the vectorial Sturm-Liouville differential equations. Some interesting relations are found.

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 study the nonlinear boundary value problem consisting of the equation y+w(t)f(y) = 0 on [a, b] and a multi-point boundary condition. By relating it to the eigenvalues of a linear Sturm-Liouville problem with a twopoint separated boundary condition, we obtain results on the existence and nonexistence of nodal solutions of this problem. We also discuss the changes of the existence of different...