Advances in Differential Equations

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

Enrico Serra and Massimo Tarallo

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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

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

First available in Project Euclid: 19 April 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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.)


Serra, Enrico; Tarallo, Massimo. A reduction method for periodic solutions of second-order subquadratic equations. Adv. Differential Equations 3 (1998), no. 2, 199--226.

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