1,721,002 research outputs found
The role of Hill equation in the study of torsional instability in suspension bridge models, Lecture notes of seminario interdisciplinare di matematica. Ediz. inglese
No full textThe present survey aims to highlight how the theory of Hill equation turns out to be a crucial tool of investigation when dealing with torsional stability in suspension bridges models. More precisely, we first recall some basic facts about Hill stability and instability domains and then we explain how these results allow to give some theoretical answers concerning the origin of torsional instability, the shape of torsional oscillations and the rule governing the energy transfer between different oscillating modes
On the second solution to a critical growth Robin problem
Full text linkWe investigate the existence of the second mountain-pass solution to a Robin problem, where the equation is at critical growth and depends on a positive parameter . More precisely, we determine existence and nonexistence regions for this type of solutions, depending both on and on the parameter in the boundary conditions
Su alcune equazioni ellittiche e paraboliche di ordine superiore con condizioni al contorno di Steklov
No full textOn the sign of solutions to some linear parabolic biharmonic equations
No full textWe study the sign of the solution of a linear parabolic biharmonic Cauchy problem in by varying both the source and the initial datum. Eventual local positivity is proved under different assumptions and the problem of global positivity is discussed
Higher order Hardy-Rellich inequalities with boundary remainder terms
No full textWe determine boundary remainder terms for some higher order Hardy-Rellich inequalities involving the polyharmonic operator . The results are proved by studying suitable auxiliary boundary eigenvalue problems, the optimal constants found may not be the classical Hardy-Rellich one
A note on some nonlinear fourth order differential equations
No full textFor a family of fourth order semilinear ordinary dffierential equations we discuss some fundamental issues, such as global continuation of solutions and their qualitative behavior. The note is the summary of a communication given at the XIX Congress of U.M.I. (Bologna - September 12-17, 2011
A qualitative explanation of the origin of torsional instability in suspension bridges
Full text linkWe consider a mathematical model for the study of the dynamical behavior of suspension bridges. We show that internal resonances, which depend on the bridge structure only, are the origin of torsional instability. We obtain both theoretical and numerical estimates of the thresholds of instability. Our method is based on a finite dimensional projection of the phase space which reduces the stability analysis of the model to the stability of suitable Hill equations. This gives an answer to a long-standing question about the origin of torsional instability in suspension bridge
Improved higher order Poincaré inequalities on the hyperbolic space via hardy-type remainder terms
No full textThe paper deals about Hardy-type inequalities associated with the following higher order Poincar\'e inequality: \left( \frac{N-1}{2} \right)^{2(k -l)} := \inf_{ u \in C^{\infty}_{0}(\mathbb{H}^{N} ) \setminus \{0\}} \frac{\int_{\hn} |\nabla_{\hn}^{k} u|^2 \ dv_{\hn}}{\int_{\hn} |\nabla_{\hn}^{l} u|^2 \ dv_{\hn} }\,, where are integers and \hn denotes the hyperbolic space. More precisely, we improve the Poincar\'e inequality associated with the above ratio by showing the existence of Hardy-type remainder terms. Furthermore, when and the existence of further remainder terms are provided and the sharpness of some constants is also discussed. As an application, we derive improved Rellich type inequalities on upper half space of the Euclidean space with non-standard remainder terms
Local regularity of weak solutions of semilinear parabolic systems with critical growth
No full textWe show that, under so called controllable growth conditions, any weak solution in the energy class of the semilinear parabolic system , is locally regular. Here, A is an elliptic matrix differential operator of order 2m. The result is proved by writing the system as a system with linear growth in but with "bad" coefficients and by means of a continuity method, where the time serves as parameter of continuity. We also give a partial generalization of previous work of the second author and von Wahl to Navier boundary condition
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