Infinitely many solutions to fourth order superlinear periodic problems

Authors:
Monica Conti, Susanna Terracini and Gianmaria Verzini

Translated by:

Journal:
Trans. Amer. Math. Soc. **356** (2004), 3283-3300

MSC (2000):
Primary 34B15; Secondary 58E05, 47J10

DOI:
https://doi.org/10.1090/S0002-9947-03-03514-1

Published electronically:
December 12, 2003

MathSciNet review:
2052950

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Abstract | References | Similar Articles | Additional Information

Abstract: We present a new min-max approach to the search of multiple -periodic solutions to a class of fourth order equations

where is continuous, -periodic in and satisfies a superlinearity assumption when . For every , we prove the existence of a -periodic solution having exactly zeroes in .

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Additional Information

**Monica Conti**

Affiliation:
Dipartimento di Matematica del Politecnico, piazza Leonardo da Vinci, 32 - 20133 Milano (I), Italy

Email:
monica.conti@polimi.it

**Susanna Terracini**

Affiliation:
Dipartimento di Matematica e Applicazioni, Università di Milano Bicocca, Via Bicocca degli Arcimboldi 8, 20126 Milano (I), Italy

Email:
suster@matapp.unimib.it

**Gianmaria Verzini**

Affiliation:
Dipartimento di Matematica del Politecnico, piazza Leonardo da Vinci, 32 - 20133 Milano (I), Italy

Email:
gianmaria.verzini@polimi.it

DOI:
https://doi.org/10.1090/S0002-9947-03-03514-1

Keywords:
Oscillating solutions,
fourth order equations,
boundary value problems,
variational methods

Received by editor(s):
May 25, 2001

Received by editor(s) in revised form:
March 21, 2003

Published electronically:
December 12, 2003

Additional Notes:
This research was supported by MURST project “Metodi Variazionali ed Equazioni Differenziali Non Lineari”

Article copyright:
© Copyright 2003
American Mathematical Society