This paper presents analogs, for certain mixed boundary-value problems, of the spectral and oscillatory properties exhibited by classical Sturm-Liouville systems. ‘l’he usual analysis of the Sturm-Liouville eigenvalue problem is based on special ad hoc methods. In contrast, Gantmacher and Krein [3; see also references therein] showed that these fundamental spectral properties are direct consequ...

Many practical problems can be formulated as convex optimization problems over the cone of nonnegative univariate polynomials. We use a cutting plane method for solving this type of optimization problems in primal form. Therefore, we must be able to verify whether a polynomial is nonnegative, i.e. if it does not have real roots or all real roots are multiple of even order. In this paper an effi...

The variational iterationmethod VIM 1–4 and homotopy perturbationmethod HPM 5– 8 , proposed byHe, are powerful analytical methods for various kinds of linear and nonlinear problems. For example, the variational iteration method has been applied to autonomous ordinary differential equation 9 and delay differential equation 10 . Abdou and Soliman applied this method to Schrodinger-KDV, generalize...

  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.

This paper examines and develops matrix methods to approximate the eigenvalues of a fourth order Sturm-Liouville problem subjected to a kind of fixed boundary conditions, furthermore, it extends the matrix methods for a kind of general boundary conditions. The idea of the methods comes from finite difference and Numerov’s method as well as boundary value methods for second order regular Sturm-L...