In the case the functional is not bounded below, i.e., L 2 supcritical case, some new difficulties arise. Firstly, since λ λ is unknown, it is impossible to construct the corresponding Nehari manifold. Secondly, it is not easy to obtain the boundedness of the Palais-Smale sequence. Furthermore, verifying the compactness of the Palais-Smale sequence is challenging because the embedding H 1 ( R N ) ↪ ↪ L 2 ( R N ) is not compact. In 1997, Louis Jeanjean using the following transform: