The Lyapunov-Schmidt reduction method and its variants are usually used to construct solutions for elliptic problems without small parameters. In Chapter 4, these methods are adapted to study the Schrodinger equations with subcritical growth. The results in Chapter 4 show that the non-compactness of some elliptic problems may give rise to the existence of infinitely many positive solutions whose energy can be arbitrarily large. Such results cannot be obtained by using the abstract critical points theories.