A variational approach to a class of nonlinear eigenvalue problems.
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- Proc. Amer. Math. Soc. 29 (1971), 272-276 Request permission
Abstract:
Let f be a real-valued differentiable function defined on the real reflexive Banach space X. The problem of minimizing f over a subset of X is investigated under the following mild monotonicity assumption on the derivative $f’$ of f: if $\{ {u_n}\}$ is a sequence in X converging weakly to some $u \in X$, then $\lim \sup (f’{u_n},{u_n} - u) \geqq 0$ . The eigenvalue problem $f’u = \lambda g’u$ for some $\lambda \in {R^1}$, with $g’$ being the derivative of a further function g, is then reduced to that first question.References
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Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 29 (1971), 272-276
- MSC: Primary 49.10; Secondary 47.00
- DOI: https://doi.org/10.1090/S0002-9939-1971-0284890-3
- MathSciNet review: 0284890