Calculating Branching Behavior of Boundary-Value Problems

Abstract

The main topic of this chapter is the calculation of branching behavior of the one-parameter family of two-point boundary-value problems As usual, the variable y (t) consists of n scalar functions y ₁ (t),…,y _n (t). The right-hand side f(t, y, λ) is a vector function; the boundary conditions [the second equation (6.1)] consist of n scalar equations, The independent variable t (a ≤ t ≤ b) need not be time; accordingly, the derivative with respect to t is denoted by a prime ′ rather than a dot: y′ = dy/dt. The bifurcation parameter λ can occur in the boundary conditions: However, because the methods discussed in this chapter are not affected by the dependence of r on λ, the notation r(y (a), y (b)) of equation (6.1) will be retained.