Advances in Differential Equations

A reduction method for periodic solutions of second-order subquadratic equations

Enrico Serra and Massimo Tarallo

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Abstract

The problem of the search for periodic solutions to certain second-order scalar subquadratic equations is reduced, by means of a variational argument, to the study of a real function of one variable, the "reduction function" of the problem. Existence and multiplicity of solutions for the original problem and for its perturbations are linked to the properties of the reduction function. Equivalent conditions for the perturbability of the problem as well as genericity results and descriptions of the range of the differential operator are obtained. Applications cover equations with oscillating or bounded nonlinearities or strongly resonant problems.

Article information

Source
Adv. Differential Equations Volume 3, Number 2 (1998), 199-226.

Dates
First available in Project Euclid: 19 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.ade/1366399896

Mathematical Reviews number (MathSciNet)
MR1750418

Zentralblatt MATH identifier
0955.34031

Subjects
Primary: 34C25: Periodic solutions
Secondary: 47J30: Variational methods [See also 58Exx] 58E05: Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirel m an) theory, etc.)

Citation

Serra, Enrico; Tarallo, Massimo. A reduction method for periodic solutions of second-order subquadratic equations. Adv. Differential Equations 3 (1998), no. 2, 199--226. https://projecteuclid.org/euclid.ade/1366399896.


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