Periodic solutions of weakly coupled superlinear systems

Fonda, Alessandro; Sfecci, Andrea

doi:10.1016/j.jde.2015.09.056

Cited by 40 publications

(24 citation statements)

References 19 publications

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“…It has been shown, indeed, that the singularities of this type provide a behavior of the solutions which resembles the situation encountered while dealing with superlinear systems (see, e.g. [1,2,3,6,7,8,9,10,11,12,13]). In the same spirit, the existence of subharmonic solutions can also be easily obtained, but we will avoid such a discussion, for briefness.…”

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confidence: 78%

Multiple periodic solutions of Hamiltonian systems confined in a box

Fonda¹,

Sfecci²

2017

Discrete &Amp; Continuous Dynamical Systems - A

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We consider a nonautonomous Hamiltonian system, T -periodic in time, possibly defined on a bounded space region, the boundary of which consists of singularity points which can never be attained. Assuming that the system has an interior equilibrium point, we prove the existence of infinitely many T -periodic solutions, by the use of a generalized version of the Poincaré -Birkhoff theorem.with a i,j ∈ R ∪ {−∞, +∞}. This means that R can be either a rectangle or an unbounded set, like a quadrant, a half-plane, or even the whole plane R 2 .We assume that the Hamiltonian function may be decomposed as2010 Mathematics Subject Classification. 34C25.

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confidence: 78%

Multiple periodic solutions of Hamiltonian systems confined in a box

Fonda¹,

Sfecci²

2017

Discrete &Amp; Continuous Dynamical Systems - A

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“…The same argument can be obtained by glueing together some guiding curves in the plane (x, y) following an idea introduced in [12] and developed in [13,14,21] in different situations. Figure 2b illustrates this idea.…”

Section: Lemma 24mentioning

confidence: 95%

“…The functions v n = x n / x n ∞ solve equation (14), which we rewrite in a simpler form v n + h n (t, v n ) = 0 ,…”

Section: Proof Of Claims 212 and 213mentioning

confidence: 99%

Double resonance for one-sided superlinear or singular nonlinearities

Sfecci

2016

Annali di Matematica

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We deal with the problem of existence of periodic solutions for the scalar differential equation x + f (t, x) = 0 when the asymmetric nonlinearity satisfies a one-sided superlinear growth at infinity. The nonlinearity is asked to be next to resonance and a Landesman-Lazer type of condition will be introduced in order to obtain a positive answer. Moreover we provide also the corresponding result for equations with a singularity and asymptotically linear growth at infinity, showing a further application to radially symmetric systems.

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“…, In this case, (4.2) is a superlinear Hamiltonian system. Under these conditions, it was proved in [12] that (4.2) has infinitely many periodic solutions by using Theorem 4.1. Theorems 1.1 and 1.2 in the present paper can also be extended to a weakly coupled Hamiltonian system of the type …”

Section: Remarksmentioning

confidence: 99%