BOUNDARY VALUE PROBLEMS VIA AN INTERMEDIATE VALUE THEOREM

L2-transforms for boundary value problems

In this article, we will show the complex inversion formula for the inversion of the L2-transform and also some applications of the L2, and Post Widder transforms for solving singular integral equation with trigonometric kernel. Finally, we obtained analytic solution for a partial differential equation with non-constant coefficients.

An Intermediate Value Theorem for the Arboricities

Let G be a graph. The vertex edge arboricity of G denoted by a G a1 G is the minimum number of subsets into which the vertex edge set of G can be partitioned so that each subset induces an acyclic subgraph. Let d be a graphical sequence and let R d be the class of realizations of d. We prove that if π ∈ {a, a1}, then there exist integers x π and y π such that d has a realization G with π G z if...

Approximating Initial-Value Problems with Two-Point Boundary-Value Problems: BBM-Equation

A differential intermediate value theorem

In this survey paper, we outline the proof of a recent differential intermediate value theorem for transseries. Transseries are a generalization of power series with real coefficients, in which one allows the recursive appearance of exponentials and logarithms. Denoting by T the field of transseries, the intermediate value theorem states that for any differential polynomials P with coefficients...

Perhaps the Intermediate Value Theorem

In the context of intuitionistic real analysis, we introduce the set F consisting of all continuous functions φ from [0, 1] to R such that φ(0) = 0 and φ(1) = 1. We let I0 be the set of all φ in F for which we may find x in [0, 1] such that φ(x) = 12 . It is well-known that there are functions in F that we can not prove to belong to I0, and that, with the help of Brouwer’s Continuity Principle ...