EIGENVALUE PROBLEMS FOR SINGULAR ODES

Singular boundary value problems for ODEs

This paper is concerned with the numerical solution of a system of ordinary di erential equations ODEs y Sy t f t y p on an inter val b subject to boundary conditions g y y b p The ODEs have a coe cient that is singular at t but it is assumed that the boundary value problem BVP has a smooth solution Some popular methods for BVPs evaluate the ODEs at t This paper deals with the practical issues ...

Numerical Solution of singular Eigenvalue Problems for ODEs with a Focus on Problems Posed on Semi-Infinite Intervals

Existence of Positive Solutions for Singular Eigenvalue Problems

In this paper, we discuss the existence, nonexistence, and multiplicity of positive solutions for a class of singular eigenvalue problems. Some of our theorems are new, while others extend earlier results obtained by Zhang and Kong [12]. The interesting point is that the authors obtain the relation between the existence of solutions and the parameter λ. The arguments are based on the fixed poin...

Singular Eigenvalue Problems for Second Order Linear Ordinary Differential Equations

We consider linear differential equations of the form (p(t)x′)′ + λq(t)x = 0 (p(t) > 0, q(t) > 0) (A) on an infinite interval [a,∞) and study the problem of finding those values of λ for which (A) has principal solutions x0(t;λ) vanishing at t = a. This problem may well be called a singular eigenvalue problem, since requiring x0(t;λ) to be a principal solution can be considered as a boundary co...

Multigrid Methods for Nearly Singular Linear Equations and Eigenvalue Problems

The purpose of this paper is to develop a convergence theory for multigrid methods applied to nearly singular linear elliptic partial differential equations of the type produced from a positive definite system by a shift with the identity. One of the important aspects of this theory is that it allows such shifts to vary anywhere in the multigrid scheme, enabling its application to a wider class...