In this paper, we consider an impulsive Sturm-Lioville problem on Sturmian time scales. We investigate the existence and uniqueness of solution problem. study some spectral properties self-adjointness boundary-value Later, construct Green function for Finally, eigenfunction expansion is obtained.

abstract.   the sturm-liouville boundary value problem of the multi-order fractional differential equation  is studied. results on the existence of solutions are established. the analysis relies on a weighted function space and a fixed point theorem. an example is given to illustrate the efficiency of the main theorems.

Abstract. The Liouville tori, having an integrable metric of the form (U1(q1)− U2(q2))(dq 2 1 + dq 2 ), allow the separation of variables in the study of the Laplacian spectrum. The asymptotic analysis of the resulting Sturm-Liouville problems allows to reduce the count of the eigenvalues of the spectrum to the count of the lattice points inside a plane domain. The present paper is concerned wi...

the purpose of this article is to use the classical sampling theorem, wks sampling theorem, to deriveapproximate values of the eigenvalues of the sturm-liouville problems with eigenparameter in the boundaryconditions. error analysis is used to give estimates of the associated error. higher order approximations are also drived, which lead to more complicated computations. we give some examples a...

Given a finite set of eigenvalues regular Sturm-Liouville problem for the equation -y{\prime}{\prime}+q(x)y={\lambda}y, potential q(x) which is unknown. We show possibility to compute more without any additional information on q(x). Moreover, considering with boundary conditions y{\prime}(0)-hy(0)=0 and y{\prime}({\pi})+Hy({\pi})=0, where h, H are some constants, we complete its spectrum neithe...

A Riemannian manifold resp. a complex space X is called Liouville if it carries no nonconstant bounded harmonic resp. holomorphic functions. It is called Carathéodory, or Carathéodory hyperbolic, if bounded harmonic resp. holomorphic functions separate the points of X . The problems which we discuss in this paper arise from the following question: When a Galois covering X with Galois group G ov...