Abstract We study distributed optimal control problems, governed by space-time fractional parabolic equations (STFPEs) involving time-fractional Caputo derivatives and spatial of Sturm-Liouville type. first prove existence uniqueness solutions STFPEs on an open bounded interval their regularity. Then we show to a quadratic problem. derive adjoint problem using the right-Caputo derivative in tim...

Abstract The Sturm–Liouville differential equation is one of interesting problems which has been studied by researchers during recent decades. We study the existence a solution for partial fractional using α - ψ -contractive mappings. Also, we give an illustrative example. By -multifunctions, prove solutions inclusion version problem. Finally providing another example and some figures, try to i...

‎in this paper‎, ‎we find matrix representation of a class of sixth order sturm-liouville problem (slp) with separated‎, ‎self-adjoint boundary conditions and we show that such slp have finite spectrum‎. ‎also for a given matrix eigenvalue problem $hx=lambda vx$‎, ‎where $h$ is a block tridiagonal matrix and $v$ is a block diagonal matrix‎, ‎we find a sixth order boundary value problem of atkin...

The one-dimensional harmonic oscillator wave functions are solutions to a SturmLiouville problem posed on the whole real line. This problem generates the Hermite polynomials. However, no other set of orthogonal polynomials can be obtained from a Sturm-Liouville problem on the whole real line. In this paper we show how to characterize an arbitrary set of polynomials orthogonal on (−∞,∞) in terms...

In this paper we define the Evans function for Sturm-Liouville problems. We show that the Evans function is analytic in the spectral parameter, has zeros in one-to-one correspondence with the eigenvalues, and is under certain conditions what we call conjugate symmetric. We conclude by showing that the Evans function can be used to track the movement of the eigenvalues as the coefficients in the...

In this paper we obtain unstable even-parity eigenmodes to the static regular spherically symmetric solutions of the SU(2) Yang-Mills-dilaton coupled system of equations in 3+1 Minkowski space-time. The corresponding matrix Sturm-Liouville problem is solved numerically by means of the continuous analogue of Newton's method. The method, being the powerful tool for solving both boundary-value and...

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 establish the connection between Sturm–Liouville equations on time scales and Sturm–Liouville equations with measure-valued coefficients. Based on this connection we generalize several results for Sturm–Liouville equations on time scales which have been obtained by various authors in the past.

We present the extension of the successful Constant Perturbation Method (CPM) for Schrödinger problems to the more general class of Sturm-Liouville eigenvalue problems. Whereas the orginal CPM can only be applied to Sturm-Liouville problems after a Liouville transformation, the more general CPM presented here solves the Sturm-Liouville problem directly. This enlarges the range of applicability ...