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On the existence of eigenvalues for some nonlinear elliptic and hyperbolic problems*

Published online by Cambridge University Press:  14 November 2011

Nicola Basile  and
Michele Mininni
Nicola Basile
Affiliation:
Dipartimento di Matematica, Universita degli Studi di Bari, Via G. Fortunato, Bari 70125, Italy
Michele Mininni
Affiliation:
Dipartimento di Matematica, Universita degli Studi di Bari, Via G. Fortunato, Bari 70125, Italy
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Synopsis

In this paper some eigenvalue problems for elliptic as well as hyperbolic equations are solved. The main tool used is an abstract critical point theorem on an unbounded manifold of the form {u | (Lu, u) = constant} (where L is a nonpositive selfadjoint operator), which makes use of a linking type argument on a manifold.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 101 , Issue 3-4 , 1985 , pp. 297 - 305
Copyright
Copyright © Royal Society of Edinburgh 1985

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