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Transactions of the American Mathematical Society

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Critical point theory for nonlinear eigenvalue problems with indefinite principal part


Author: Melvyn S. Berger
Journal: Trans. Amer. Math. Soc. 186 (1973), 151-169
MSC: Primary 47H15; Secondary 58E15
DOI: https://doi.org/10.1090/S0002-9947-1973-0341210-X
MathSciNet review: 0341210
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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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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1973-0341210-X
Keywords: Nonlinear eigenvalue problems, nonlinear operator equation, semilinear elliptic boundary value problem
Article copyright: © Copyright 1973 American Mathematical Society

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