Critical point theory for nonlinear eigenvalue problems with indefinite principal part
Melvyn S. Berger · Transactions of the American Mathematical Society · 1973
A study of the nontrivial solutions of the operator equation $Lu = \lambda \Pi ’(u)$ is made, where L is a selfadjoint Fredholm operator mapping a Hilbett space H into itself, and $\Pi (u)$ is a $C’$ weakly sequentially continuous real valued functional defined on H. Applications are given to the theory of semilinear elliptic boundary value problems and periodic solutions of Hamiltonian systems.