A general method for the existence of periodic solutions of differential systems in the plane

Infinitely many subharmonic solutions for nonlinear equations with singular $ \phi $-Laplacian

“…This property and the angular feature of the fixed points obtained by Pincaré-Birkhoff twist theorem inspire us to consider a modified equation of (1) instead. We mention here that in recent, Fonda and Sfecci [17] developed the so-called admissible spiral method, a tool introduced by the same authors in [18], to prove the existence of infinitely many periodic solutions for weakly coupled superlinear second order systems. The argument for the spiral property is also used to obtain the existence of infinitely many periodic solutions for superlinear second order equation 2without the sign condition (G 0 ) [32].…”

Infinitely many periodic solutions of planar Hamiltonian systems via the Poincaré–Birkhoff theorem

“…Since g only satisfies condition (h 1 ), we know that ∇ z H(t, z) does not satisfy the semilinear condition as in [11] or the superlinear condition as in [4].…”

“…For instance, using the Poincaré-Bohl fixed point theorem, Fonda and Sfecci [11] studied the existence of periodic solutions of planar Hamiltonian systems Jz = ∇ z H(t, z), z = (x, y) ∈ R 2 , (…”

“…When ∇ z H(t, z) satisfies some semilinear conditions at infinity, it was proved in [11] that (1.2) has at least one T-periodic solution. Using a generalized Poincaré-Bikhoff fixed point theorem, Boscaggin [4] studied the multiplicity of periodic solutions of (1.2), provided that ∇ z H(t, z) satisfies some superlinear condition at infinity.…”

Double resonance for one-sided superlinear or singular nonlinearities

“…By the construction of some guiding functions we can prove the following estimates. Notice that the use of guiding functions was adopted also in [15], by the use of a general method presented by Fonda and the author in [12]. Lemma 3.6 There exists N (N 0 ) > N 0 such that every T -periodic solution of (23) such that N (x(t 0 ), y(t 0 )) > N (N 0 ) at a certain time t 0 is a N 0 -large solution.…”