Critical point theory for nonlinear eigenvalue problems with indefinite principal part

Berger, Melvyn S.

doi:10.1090/S0002-9947-1973-0341210-X

Critical point theory for nonlinear eigenvalue problems with indefinite principal part
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Trans. Amer. Math. Soc. 186 (1973), 151-169 Request permission

Abstract:

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.

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