Abstract
This chapter focuses on linearity and nonlinearity in the theory of G-convergence. It discusses the main lines of the theory of G-convergence for ordinary differential equations. It deals in particular with the various definitions of G-convergence, with the equivalence properties and with the phenomena of nonlinearity that can arise in the theory. Even if the theory does not depend on De Giorgi's abstract definition, it seems better to unify the different approaches starting from De Giorgi's abstract definition. The chapter presents definitions of G-convergence. An analysis of the problems that arise in the theory is presented. A discussion of the single problems is provided. The chapter also describes an extension toward a general theory and presents a short discussion of the results of the general theory.
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