The objective of the current study is to develop a simple formula to estimate the fundamental vibration period of tall buildings for using in equivalent lateral force analysis specified in building codes. The method based on Sturm-Liouville differential equation is presented here for estimating the fundamental period of natural vibration. The resulting equation, based on the continuum represent...

In this study, fractional differential transform method (FDTM), which is a semi analytical-numerical technique, is used for computing the eigenelements of the Sturm-Liouville problems of fractional order. The fractional derivatives are described in the Caputo sense. Three problems are solved by the present method. The calculated results are compared closely with the results obtained by some exi...

We study three internally connected Sturm-Liouville problems for nonlinear ordinary differential equations that are motivated by the problem of aeroelastic instability. Solutions are analyzed and asymptotic results are presented. A numerical study using a development of simple shooting reveals the spectrum and corresponding eigenfunctions.

ABSTRACT. In this paper, we establish the existence of at least three positive solutions for thirdorder impulsive Sturm-Liouville boundary value problems with p-Laplacian, by a fixed point theorem due to Avery and Peterson. We discuss our problem both for advanced and delayed arguments. An example is included to illustrate that corresponding assumptions are satisfied.

The geometric multiplicity of each eigenvalue of a self-adjoint Sturm-Liouville problem is equal to its algebraic multiplicity. This is true for regular problems and for singular problems with limit-circle endpoints, including the case when the leading coefficient changes sign.

We deal with an inverse nodal problem for p-Laplacian Sturm-Liouville equation which includes Coulomb type potential function under boundary condition depends on polynomial spectral parameter. Here, we get some asymptotic formulas of eigenvalues and nodal parameters by using a suitable Prüfer substitution. Eventually, we construct Coulomb potential by using nodal lengths. c ©2017 All rights res...

We study the relationship between the eigenvalues of separated self-adjoint boundary conditions and coupled self-adjoint conditions. Given an arbitrary real coupled boundary condition determined by a coupling matrix K we construct a one parameter family of separated conditions and show that all the eigenvalues for K and −K are extrema of the eigencurves of this family. This characterization mak...

We derive Povzner–Wienholtz-type self-adjointness results form× m matrix-valued Sturm–Liouville operators T = R [

on a special interval. We obtain some nodal parameters like nodal points and nodal lengths. In addition, we reconstruct the potential function by nodal points. Results obtained in this paper are similar to the classical Sturm–Liouville problem. However, equations of this type are considered with the condition defined at the origin. We solve the problem on the interval [1,a], that problem is not...

Under additional conditions uniqueness of the solution is proved for the following problem. Given 1) the spectrum of the Dirichlet problem for the Sturm–Liouville equation on [0, a] with real potential q(x) ∈ L2(0, a), 2) a certain part of the spectrum of the Dirichlet problem for the same equation on [ 3 , a] and 3) the potential on [0, a 3 ]. The aim is to find the potential on [ 3 , a].