ABSTRACT
In Chapter 1, we gained familiarity with the notion of stability for semilinear elliptic equations of the form (1.3). It is time to look at a concrete example. This chapter is devoted to the study of the following problem:−∆u= λeu in B,
u= 0 on ∂ B, (2.1)
where λ > 0 is a parameter and B is the unit ball of RN , N ≥ 1. Equation (2.1) bears many names: Barenblatt, Bratu, Emden, Fowler, Frank-Kamenetskii, Gelfand, and Liouville are some of the famous scientists to whom the equation has been attributed. For short, we call (2.1) the Gelfand problem.1 It arises as a (crude) model in a number of interesting physical contexts,2 one of which we outline next.
