Introduction

Continuation, embedding or homotopy methods have long served as useful tools in modern mathematics. Their use can be traced back at least to such venerated works as those of Poincaré (1881–1886), Klein (1882–1883) and Bernstein (1910). Leray & Schauder (1934) refined the tool and presented it as a global result in topology viz. the homotopy invariance of degree. The use of deformations to solve nonlinear systems of equations may be traced back at least to Lahaye (1934). The classical embedding methods may be regarded as a forerunner of the predictor-corrector methods which we will treat extensively in this book.