Generalization for Amann’s and Leggett–Williams’ three-solution theorems and applications

In this paper, some new three-solution theorems are obtained. Moreover, the famous Amann’s and Leggett–Williams’ three-solution theorems in nonlinear functional analysis can be seen as their special cases, namely these two famous theorems are united. So they are both improved. And that some new three-solution theorems are applied to ordinary differential equations, and some new existence results are obtained.  2004 Elsevier Inc. All rights reserved.