On non-linear differential equations of the second order: IV. The general equation $\ddot y + kf\left( y \right)\dot y + g\left( y \right) = bkp\left( \varphi \right)$ , φ=t+α, φ=t+α

Abstract

in Cambridge w t.We enter now on our complete account of the more general equation ij+kit(y)~+g(y)=bkp(q~), ~=t+~.The functions i t, g, p are fixed, b is non-negative, and k is large and positive.We proceed to state the long list of assumptions about it, g, p.It may help towards easier reading to imagine that it and g are polynomials and p a trigonometrical polynomial: in so far as hypotheses about the smoothness of f, g, p are concerned our arguments are not essentially different from what they would then be, and the reader may trust us to have taken care of the details.He may similarly take on trust details about * The N near U is alter Z,U , and in the extreme case when (0, t) extends to U, Nv is approximately 2 re before U.* This is used for some construction, and later discarded.B+ and B_ are not necessarily composed of continuous curves, but this does not affect our argument.

Locations

• Acta Mathematica - View - PDF