Nonlinear Eigenvalues

Abstract

In Chapter II we obtained critical sequences for the solution of

$$G'\left( u \right) = 0$$

(11.1.1)

by finding linking sets which separate the values of G or sequences of such sets. In Chapter V we applied this technique to show that one obtains solutions of (11.1.1) inside a ball or solutions of (11.1.2)

$$G'\left( u \right) = \beta u$$

((11.1.2))

on the boundary. As a result, one obtains either solutions of (11.1.1) or a rich family of eigenfunctions satisfying (11.1.2).