Problems in the Theory of Ordinary Linear Differential Equations with Auxiliary Conditions at More than Two Points

Expansion Problems of Ordinary Linear Differential Equations with Auxiliary Conditions at More than Two Points

The boundary value and expansion problems for the equation of the nth order with boundary conditions at two points have been studied by Birkhoff. t BocherJ has suggested the generalization of these results to the equation with auxiliary conditions at more than two points. Such generalization of the essential properties of the differential system has been carried out by the author, and in this p...

Introduction to the Galois Theory of Linear Ordinary Differential Equations

We define the differential Galois group of a linear homogeneous ordinary differential equation and illustrate the type of information about solutions packaged within. The initial format is classical; at the end we indicate how the results can be conceptualized geometrically.

The Picard-Vessiot Theory of Homogeneous Linear Ordinary Differential Equations.

Ordinary Differential Equations with Nonlinear Boundary Conditions

The method of lower and upper solutions combined with the monotone iterative technique is used for ordinary differential equations with nonlinear boundary conditions. Some existence results are formulated for such problems. 2000 Mathematics Subject Classification: 34A45, 34B15, 34A40.

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...