Averaging techniques for self-adjoint matrix equations on a measure chain

Self-adjoint differential-algebraic equations

Eigenvalue Comparisons for Differential Equations on a Measure Chain

The theory of u0-positive operators with respect to a cone in a Banach space is applied to eigenvalue problems associated with the second order ∆-differential equation (often referred to as a differential equation on a measure chain) given by y(t) + λp(t)y(σ(t)) = 0, t ∈ [0, 1], satisfying the boundary conditions y(0) = 0 = y(σ2(1)). The existence of a smallest positive eigenvalue is proven and...

A NOTE ON THE AVERAGING METHOD FOR DIFFERENTIAL EQUATIONS WITH MAXIMA

Substantiation of the averaging method for differential equations with maxima is presented. Two theorems on substantiates for differential equations with maxima are established.

Factorization of self-adjoint ordinary differential equations

Keyword: Factorization method Self-adjoint differential equations Eigenvalue problems This paper deals with the factorization of self-adjoint differential operators Lð2nÞ 1⁄4 1 q d n dx qb d n dx , and their spectral type differential equations. Sufficient conditions of factorization are reported. A large class of differential operators and equations that can be factorized is obtained. The fact...

An Extended-matrix Preconditioner for Nonself-adjoint Nonseparable Elliptic Equations∗

In a previous paper we proposed a preconditioning technique that generalizes an idea by M. Griebel. In this generalization, although all considerations are presented in a very general algebraic framework, the main idea behind them is to use as preconditioner a rectangular matrix constructed with the transfer operators between successive discretization levels of the initial problem. In this way ...