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.

in this paper we apply the homotopy perturbation method to derive the higher-order asymptotic distribution of the eigenvalues and eigenfunctions associated with the linear real second order equation of sturm-liouville type on $[0,pi]$ with neumann conditions $(y'(0)=y'(pi)=0)$ where $q$ is a real-valued sign-indefinite number of $c^{1}[0,pi]$ and $lambda$ is a real parameter.

The Sturm–Liouville hierarchy of evolution equations was introduced in [Adv. Nonlinear Stud. 11 (2011), 555–591] and includes the Korteweg–de Vries and the Camassa– Holm hierarchies. We discuss some solutions of this hierarchy which are obtained as limits of algebro-geometric solutions. The initial data of our solutions are (generalized) reflectionless Sturm–Liouville potentials [Stoch. Dyn. 8 ...

Sturm-Liouville Theory Christopher J. Adkins Master of Science Graduate Department of Mathematics University of Toronto 2014 A basic introduction into Sturm-Liouville Theory. We mostly deal with the general 2ndorder ODE in self-adjoint form. There are a number of things covered including: basic asymptotics, properties of the spectrum, interlacing of zeros, transformation arguments...

In this article, we consider dissipative Sturm–Liouville operators in the limit-circle case on time scales. Then, using the Livšic’s Theorem, we prove the completeness of the system of root vectors for dissipative Sturm–Liouville operators. 2013 Elsevier Inc. All rights reserved.

We consider a regular indefinite Sturm-Liouville problem with two self-adjoint boundary conditions, one being affinely dependent on the eigen-parameter. We give sufficient conditions under which a basis of each root subspace for this Sturm-Liouville problem can be selected so that the union of all these bases constitutes a Riesz basis of a corresponding weighted Hilbert space.

Regular and singular Sturm-Liouville problems (SLP) are studied including the continuous and differentiable dependence of eigenvalues on the problem. Also initial value problems (IVP) are considered for the SL equation and for general first order systems.

Oscillation and nonoscillation properties of second order Sturm–Liouville dynamic equations on time scales attracted much interest. These equations include, as special cases, second order self-adjoint differential equations as well as second order Sturm–Liouville difference equations. In this paper we consider a given (homogeneous) equation and a corresponding equation with forcing term. We giv...

This paper gives the analysis and numerics underlying a shooting method for approximating the eigenvalues of nonselfadjoint Sturm-Liouville problems. We consider even order problems with (equally divided) separated boundary conditions. The method can nd the eigenvalues in a rectangle and in a left half-plane. It combines the argument principle with the compound matrix method (using the Magnus e...