Advances in Differential Equations
- Adv. Differential Equations
- Volume 3, Number 2 (1998), 199-226.
A reduction method for periodic solutions of second-order subquadratic equations
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.
Adv. Differential Equations Volume 3, Number 2 (1998), 199-226.
First available in Project Euclid: 19 April 2013
Permanent link to this document
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.https://projecteuclid.org/euclid.ade/1366399896