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Nonlinear problems with strong resonance at infinity: an abstract theorem and applications*

Published online by Cambridge University Press:  14 November 2011

A. Capozzi  and
A. Salvatore
A. Capozzi
Affiliation:
Dipartimento di Matematic, Università degli Studi di Bari, Bari, Italy
A. Salvatore
Affiliation:
S.I.S.S.A., Trieste, Italy
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Synopsis

In this paper, we consider the equation

where A is a linear operator, N = ψ′ with ψ ∈ C1(E, R), and E is an Hilbert space. We suppose that N has a derivative at infinity N′(∞) and that 0 belongs to the spectrum of A–N′(∞). We prove an abstract theorem for multiplicity of solutions for the above equation. We then apply this theorem to the study of periodic solutions of Hamiltonian systems and of semilinear wave equations when the period is prescribed.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 99 , Issue 3-4 , 1985 , pp. 333 - 345
Copyright
Copyright © Royal Society of Edinburgh 1985

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