Gianni Arioli

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The existence of nontrivial solutions of quasilinear elliptic equations at critical growth is proved. The solutions are obtained by variational methods: as the corresponding functional is nonsmooth, the analysis of Palais-Smale sequences requires suitable generalizations of the techniques involved in the study of the corresponding semilinear problem with(More)
We study a semilinear fourth order elliptic problem with exponential nonlinearity. Motivated by a question raised in [Li], we partially extend known results for the corresponding second order problem. Several new difficulties arise and many problems still remain to be solved. We list the ones we feel particularly interesting in the final section.(More)
The coupling between cardiac mechanics and electric signaling is addressed in a nonstandard framework in which the electrical potential dictates the active strain (not stress) of the muscle. The physiological and mathematical motivations leading us to this choice are illustrated. The propagation of the electric signal is assumed to be governed by the(More)
We develop some computer-assisted techniques for the analysis of stationary solutions of dissipative partial differential equations, their stability, as well as bifurcation diagrams. As a case study, these methods are applied to the Kuramoto-Sivashinski equation. This equation has been investigted extensively, and its bifurcation diagram is well known from(More)
We investigate entire radial solutions of the semilinear biharmonic equation ∆u = λ exp(u) in Rn, n ≥ 5, λ > 0 being a parameter. We show that singular radial solutions of the corresponding Dirichlet problem in the unit ball cannot be extended as solutions of the equation to the whole of Rn. In particular, they cannot be expanded as power series in the(More)
We analyze a model of electric signalling in biological tissues and prove that this model admits a travelling wave solution. Our result is based on a new technique for computing rigorous bounds on the stable and unstable manifolds at an equilibrium point of a dynamical system depending on a parameter. 1. Modeling, motivations and main result The(More)
All attempts of aeroelastic explanations for the torsional instability of suspension bridges have been somehow criticised and none of them is unanimously accepted by the scientific community. We suggest a new nonlinear model for a suspension bridge and we perform numerical experiments with the parameters corresponding to the collapsed Tacoma Narrows Bridge.(More)
Variational methods have recently been applied to the search of homoclinic solutions for first and second order Hamiltonian systems (see e.g. [1, 2, 3, 6] and the references therein). Homoclinic solutions obtained there are mountain pass points for suitable functionals, namely either the Lagrangian functional or its dual with respect to the Legendre(More)