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On the periodic Fučik spectrum and a superlinear Sturm–Liouville equation

Published online by Cambridge University Press:  14 November 2011

Djairo G. Figueiredo  and
Bernhard Ruf
Djairo G. Figueiredo
Affiliation:
IMECC, Universidade Estadual di Campinas, 13081 Campinas, S.P., Brasil
Bernhard Ruf
Affiliation:
Dip. di Matematica, Università degli Studi, Via Saldini 50, 20133 Milano, Italy
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Synopsis

In the first part of the paper a variational characterisation of the periodic eigenvalues (the so-called Fučik spectrum) of a semilinear, positive homogeneous Sturm–Liouville equation is given. The proof relies on the S1-invariance of the equation.

In the second part a nonlinear Sturm–Liouville equation with, typically, an exponential nonlinearity is considered. It is proved that under certain conditions this equation is solvable for arbitrary forcing terms. The proof uses a comparison of the minimax levels of the functional associated to this equation with suitable values in the Fučik spectrum.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 123 , Issue 1 , 1993 , pp. 95 - 107
Copyright
Copyright © Royal Society of Edinburgh 1993

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