8,872 research outputs found
Positive periodic solutions for planar differential systems with repulsive singularities on the axes
No full textIn this paper we provide an existence result of periodic solutions to planar systems having a repulsive singularity on both the axes. We require a nonresonance assumption, related to the spectrum of the periodic problem associated to the Steen's planar system **formula** which is isochronous (see [15]). As a particular case we obtain the existence of periodic solutions to a periodically perturbed Steen's planar system
Nonresonance conditions for radial solutions of nonlinear neumann elliptic problems on annuli
No full textAn existence result to some nonlinear Neumann elliptic problems defined on balls has been provided recently by the author
in [21]. We investigate, in this paper, the possibility of extending such
a result to annuli
Periodic Impact Motions at Resonance of a Particle Bouncing on Spheres and Cylinders
No full textWe investigate the existence of periodic trajectories of a particle, subject to a central force, which can hit a sphere or a cylinder. We will also provide a Landesman–Lazer-type condition in the case of a nonlinearity satisfying a double resonance condition. Afterwards, we will show how such a result can be adapted to obtain a new result for the impact oscillator at double resonance
Some existence results for boundary value problems : a promenade along resonance
No full textI present many existence result to many boundary value problems, in particular periodic problems and Neumann elliptic problems. The results use the method of the topological degree theory. In the thesis different problems are treated: planar systems, systems with a singularity, impact oscillators, coupled oscillators and radial elliptic problems
A nonresonance condition for radial solutions of a nonlinear Neumann elliptic problem
No full textWe prove an existence result for radial solutions of a Neumann elliptic problem whose
nonlinearity asymptotically lies between the first two eigenvalues. To this aim, we
introduce an alternative nonresonance condition with respect to the second eigenvalue
which, in the scalar case, generalizes the classical one, in the spirit of Fonda et al. (1991).
Our approach also applies for nonlinearities which do not necessarily satisfy a subcritical
growth assumption
From isochronous potentials to isochronous systems
No full textThere is a wide literature involving the study of isochronous equations of the type **formula**
where V is a C2-function. In this paper we show how the kinetic energy **formula** can be modified still preserving the isochronicity property of the corresponding system. More generally we provide estimates for the periods, and show an application to the Steen's equation and other systems related to the anharmonic potential **formula**
Double resonance for one-sided superlinear or singular nonlinearities
No full textWe 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
Multiple periodic solutions of hamiltonian systems confined in a box
No full textWe 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
On the structure of radial solutions for some quasilinear elliptic equations
No full textIn this paper we study entire radial solutions for the quasilinear p-Laplace equation **formula** where k is a radial positive weight and the nonlinearity behaves e.g. as **formula** with **formula**. In particular we focus our attention on solutions (positive and sign changing) which are infinitesimal at infinity, thus providing an extension of a previous result by Tang (2001)
Periodic solutions of a system of coupled oscillators with one-sided superlinear retraction forces
No full textWe generalize the phase-plane method approach introduced in [9] to the case of higher dimensions. To this aim, the phase-space is assumed to be decomposable as a product of planes, where the cor- responding components of the solutions can be controlled by means of suitable plane curves. We then apply our general result to the periodic problem associated to a system of coupled oscillators, with retraction forces having a linear growth, or with one-sided superlinear nonlineari- ties
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