Periodic solutions of Duffing's equations with superquadratic potential

Multiplicity results for periodic solutions of second order ODEs with asymmetric nonlinearities

“…This definition of subharmonic solutions of order m corresponds to that considered in [38] and was used in [11], [12], [13]. On the other hand, note that this is not exactly the definition of subharmonic solutions as considered for instance in [33].…”

“…This will be guaranteed by smoothness or local lipschitz assumptions in the x-variable. The situation in which the uniqueness of the solutions for the initial problems is not ensured can be treated as well by a standard approximation technique described in [11]. However, the conclusion of some results should be slightly modified with respect to the number of the periodic solutions we find (see Remark 5 in Section 8).…”

Monotone twist maps and periodic solutions of systems of Duffing type

“…Typically these extensions employ sophisticated versions of the Poincaré-Birkhoff theorem and the condition of monotone twist is not required. In this direction we mention the paper by Ding and Zanolin [3] and the references therein.…”

Infinitely many solutions to superlinear second order m-point boundary value problems

“…Thus, u has at least k -1 zeros in (0, 1), and at most k zeros in ( Superlinear problems with classical boundary value conditions have been considered in many papers, particularly in the second and fourth order cases, with either periodic or separated boundary conditions, see for example [2][3][4][5][6][7][8][9][10][11] and the references therein. Specifically, the second order periodic problem is considered in [2,3], while [4][5][6][7] consider problems with separated boundary conditions, and results similar to Theorem 1.1 were obtained in each of these papers. The fourth order periodic problem is considered in [8][9][10].…”