In this paper we have considered the question of the existence of the solution of a pair of coupled ordinary differential equations depending on a parameter s. By using a corollary of the Schauder-Tychonoff fixed point theorem, and some hard analysis — needed to cover essentially the range of s near s=0 — we were able to show that all the conditions for the theorem could be fulfilled. Hence existence for all values of s>0 was established. We also considered the question of uniqueness. There we used a number of rough estimates. In this way the calculations are largely simplified, but it is then not possible to prove uniqueness for all values of s. We only proved it for s>2.33.
|Journal||Indagationes Mathematicae A: Mathematical sciences|
|Publication status||Published - 1984|